TAKEUCHI Mitsuhiro 竹内光弘

… Alternative Names

竹内光弘

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Researcher Number	00015950
Other IDs
Affiliation (based on the past Project Information) *help	2004 – 2009: University of Tsukuba, Graduate School of Pure and Applied Sciences, Professor, 大学院・数理物質科学研究科, 教授 1991 – 2003: 筑波大学, 数学系, 教授 1988 – 1990: 筑波大学, 数学系, 助教授 1986: 筑波大学, 数学系, 助教授
Review Section/Research Field	Principal Investigator Algebra / Algebra / 代数学・幾何学 Except Principal Investigator Algebra / 代数学・幾何学 / Algebra / Global analysis / Geometry
Keywords	Principal Investigator 量子群 / ホップ代数 / braided category / 組紐カテゴリー / 頂点作用素代数 / 有限群 / コサイクル変形 / 代数群 / cylinder matrix / biFrobenius algebra … More / modular category / braid / Hopf algebra / quantum group / quantum matrix / ガウス分解 / 量子ガロア群 / cylinder代数 / 準結晶 / braidedホップ代数 / Kac-Moody群 / Kaplansky予想 / matched pair / ヘッケ代数 / コホモロジー / ボゾン化 / Homfly多項式 / cylinder行列 / 双フロベニウス代数 / モジュラー圏 / 結び目 / 量子行列 / 結晶基 / 余加群代数 / 森田理論 / 環論 / bialgebroid / bialgebroid, Picard-Vessiot理論 / FRT構成 / ガロア理論 / 不変量 / 作用素環 / 多元環 / リー代数 / 一般線形群 / シュバレー群 / Kac-Moody代数 / 表現論 / Virasoro代数 / KacーMoody群 / リ-代数 … More Except Principal Investigator ホップ代数 / 量子群 / Hopf algebra / 概均質ベクトル空間 / Picard-Vessiot theory / ピカール・ヴェシオ理論 / 有限単純群 / Lakshmibai-Seshadri path / path model / quantum group / 差分方程式 / Quantum group / 非可換幾何学 / algebraic group / alternating group / Lie algebra / Coxeter group / Kac-Moody group / 有限群 / 代数群 / ガロワ被覆 / C^-代数 / Kac-Takesaki作用素 / 既約ユニタリー表現 / スペクトル解析 / 非コンパクト型量子群 / フーリエ変換 / 相対不変式 / モジュライ空間 / 関数等式 / Chevalley群 / cocbcle deformation / affine group scheme / braided category / tensor category / 微分方程式 / テンソルカテゴリー / 組ひもカテゴリー / 形式群 / アフィン群 / コサイクル変形 / アフィン群スキーム / 組紐圏 / テンソル圏 / differential-difference Galois theory / Hopf-Galois theory / brided Hopf algebra / Super formal group / Super affine group / 差分ガロア理論 / 微分ガロア理論 / ホップガロア理論 / 組紐ホップ代数 / 微分・差分ガロア理論 / ポップガロア理論 / 組紐ポップ代数 / スーパー形式群 / スーパーアフィン群 / Picard-Vessiot理論 / Tanaka duality / II_1 subfactor / group cohomology / super-affine group / super-Hopf algebra / 群のコホモロジー / 部分因子環 / ホップ・ガロア拡大 / ホモロジー代数 / 淡中双対定理 / 淡中双対性 / II_1型部分因子環 / 群コホモロジー / スーパー・アフィン群スキーム / スーパー・ホップ代数 / fundamental representation / level zero / standard module / extremal weight module / quantum affine algebra / crystal base / 基本表現 / レベル・ゼロ / standard加群 / extremalウエイト加群 / アフィン量子群 / 結晶基底 / Hochschild cohomology / Hopf cohomology / Crossed product / Cocfuasi-bialgebra / Tensor equivalence / ガロア対象 / 組紐構造 / ホッホシルトコホモロジー / ホップコホモロジー / 接合積 / 余準双代数 / テンソル同値 / computer system / symmetric space / マルチクラスター計算機システム / グレプナー基底 / 数理物理学のモデル / 複素構造と表現論 / 量子ベクトル束の特性類 / 巡回(コ)ホモロジー / 調和解析学 / 量子多様体の非可換幾何 / コニタリー表現論 / 調和解析 / 代数幾何学 / ゲージ理論 / q-アナログ / ファイバー束 / 数理物理学 / ホモロジー代数学 / 非可換微分幾何学 / 量子群の表現論 / 数式処理 / ユニタリー表現 / インスタントン / 4次元球面 / 熱核 / 計算機 / 対称空間 / Relative invaliant / Fourier transform / weakly spherical homogeneous spaces / Prehomogeneous vector spaces / 弱球等質空間 / Complex structure / Noncommutative geometry / Automorphic functions / Discontiumous group / Spectral analysis of a self-adjoint operator / Hyperbolic geometry / Unitary repreoentation / 複素構造 / 保型関数論 / 不連続群 / 自己共役作用素のスペクトル解析 / 双曲幾何学 / ユニタリー表現論 / Lie algebtra / algebraic K-theory / Algebraic group / Alternating group / Algebraic K-theory / Hecke algebras / vertex operator algebras / combinatorics / monster / algebraic groups / finite simple groups / アソシェーションスキーム / ヘッケ環 / 頂点作用素代数 / 組合せ数学 / モンスター / Unitary Refrection Group / Finite Group / Association Scheme / Quantum Group / Kac-Moody Lie Algebra / グラフ / 結び目 / アダマール行列 / 量子代数 / 統計力学 / アフィン・リー代数 / 最高ウェイト加群 / スピン・モデル / フュージョン代数 / アソシエーションスキーム / コード理論 / モジュラー形式 / 鏡映群 / 相関関数 / 超幾何関数 / ユニタリ鏡映群 / アソシエーション・スキーム / カッツ・ムーディーリー環 / quasi-hereditary 多元環 / highest weight 圏 / Kac-Moody群 / 多様体 / テイツツ系 / 代数解析 / 半単純代数群 / 多元環 / ^-ホップ代数 / 淡中-辰馬型の双対定理 / 量子カシミア作用素 / 対称多元環 / 中山自己同型 / Auslander-Reiten quiver / 表現 / 有限次元多元環 / 中山環 / 大局次元 / フロベニウス多元環 / アルチン多元環 / *-ホップ代数 / テンリル積表現の分解 / カシミア作用素 / 部分因子環の指数理論 / 有限群論 / 代数的組み合わせ論 / バラグループ / meta-ablianization / approximate polynomial / SL_2 / Artinianring / representation / quantum groups / Frobenius conjecture / 井草局所ゼータ関数 / 岩沢-Tate理論 / reduction / 局所体 / Gauss写像 / Yang-Mills理論 / 調和写像 / L^2ー計量 / 反自己双対的 / ワイル共形曲率テンソル / 共形構造 / Levy processses / quantum matrices / Grothendiech group / Derived category / Cartan matrices / category equivalence / Morita contexts / 極小部分多様体 / 概素数 / フロベニウス予想 / 単純群 / 量子化 / ゼ-タ関数 / 素数分布 / ω-安定 / 単列環 / Grothendieck群 / 被覆 / カルタン行列 Less

Hopf algebras and their applications to quantum groupsPrincipal Investigator
- Principal Investigator
  
  TAKEUCHI Mitsuhiro
- Project Period (FY)
  2006 – 2009
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  University of Tsukuba
Unifying differential and difference Picard Vessiot theories by using Hopfalgebras
- Principal Investigator
  
  MASUOKA Akira
- Project Period (FY)
  2006 – 2007
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  University of Tsukuba
Generalization of Hopf-quotient theory and applications to subfactors and others
- Principal Investigator
  
  MASUOKA Akira
- Project Period (FY)
  2004 – 2005
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  University of Tsukuba
Study on the path models for extremal weight modules over a quantum affine algebra
- Principal Investigator
  
  NAITO Satoshi
- Project Period (FY)
  2002 – 2004
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  University of Tsukuba
Classification of coquasi-Hopf algebras by tensor equivalence and constructions of new braidings
- Principal Investigator
  
  MASUOKA Akira
- Project Period (FY)
  2002 – 2003
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  University of Tsukuba
Classification of Hopf algebras and quantum groups by tensor equivalences
- Principal Investigator
  
  MASUOKA Akira
- Project Period (FY)
  2000 – 2001
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  University of Tsukuba
Development from prehomogeneous vector spaces to weakly spherical homogeneous spaces
- Principal Investigator
  
  KIMURA Tatsuo
- Project Period (FY)
  1999 – 2001
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Research Field
  
  Algebra
- Research Institution
  University of Tsukuba
Irreducible unitary representation of non compact quantum group SUq(1,1) and its quantum symmetric space
- Principal Investigator
  
  MASUDA Tetsuya
- Project Period (FY)
  1999 – 2002
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Research Field
  
  Global analysis
- Research Institution
  University of Tsukuba
Research on quantum matrices and Hopf algebrasPrincipal Investigator
- Principal Investigator
  
  MITSUSHIRO Takeuchi
- Project Period (FY)
  1999 – 2002
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  University of Tsukuba
Noncommutative geometry of quantum complex upper half plane and discrete subgroup of a non-compact quantum group
- Principal Investigator
  
  MASUDA Tetsuya
- Project Period (FY)
  1997 – 1998
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  University of Tsukuba
量子群とリー代数の表現論Principal Investigator
- Principal Investigator
  
  竹内光弘
- Project Period (FY)
  1996
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  University of Tsukuba
フロベニウス多元環のガロワ被覆と変形理論の研究
- Principal Investigator
  
  山形邦夫
- Project Period (FY)
  1996
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  University of Tsukuba
非コンパクト型量子群SUq(1,1)の既約ユニタリー表現の完全分類
- Principal Investigator
  
  増田哲也
- Project Period (FY)
  1996
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  University of Tsukuba
Group theory and related topics
- Principal Investigator
  
  YAMAKI Hiroyoshi
- Project Period (FY)
  1996 – 1998
- Research Category
  
  Grant-in-Aid for Scientific Research (A)
- Research Field
  
  Algebra
- Research Institution
  Kumamoto University
A research of algebraic groups and Lie algebras
- Principal Investigator
  
  MORITA Jun
- Project Period (FY)
  1996
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Research Field
  
  Algebra
- Research Institution
  University of Tsukuba
量子群と代数群の表現論Principal Investigator
- Principal Investigator
  
  竹内光弘
- Project Period (FY)
  1995
- Research Category
  
  Grant-in-Aid for General Scientific Research (B)
- Research Field
  
  Algebra
- Research Institution
  University of Tsukuba
量子群SUq(1,1)のユニタリー表現のテンリル積の分解
- Principal Investigator
  
  増田哲也
- Project Period (FY)
  1995
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  University of Tsukuba
フロベニウス多元環のガロワ被覆と変形理論の研究
- Principal Investigator
  
  山形邦夫
- Project Period (FY)
  1995
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  University of Tsukuba
表現論の観点からの量子群の研究Principal Investigator
- Principal Investigator
  
  竹内光弘
- Project Period (FY)
  1994
- Research Category
  
  Grant-in-Aid for Scientific Research on Priority Areas
- Research Institution
  University of Tsukuba
群の表現と方程式の研究およびその応用
- Principal Investigator
  
  森田純
- Project Period (FY)
  1994
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  University of Tsukuba
パラグループの代数構造に関する群論的研究
- Principal Investigator
  
  増田哲也
- Project Period (FY)
  1994
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  University of Tsukuba
調和写像の微分幾何学
- Principal Investigator
  
  中川久雄
- Project Period (FY)
  1993
- Research Category
  
  Grant-in-Aid for General Scientific Research (B)
- Research Field
  
  Geometry
- Research Institution
  University of Tsukuba
局所体上の概均質ベクトル空間の理論
- Principal Investigator
  
  木村達雄
- Project Period (FY)
  1993
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  University of Tsukuba
Co-operative Research in Representation Theory
- Principal Investigator
  
  KAWANAKA Noriaki
- Project Period (FY)
  1993 – 1995
- Research Category
  
  Grant-in-Aid for Co-operative Research (A)
- Research Field
  
  Algebra
- Research Institution
  OSAKA UNIVERSITY
4次元多様体の幾何学とゲージ理論
- Principal Investigator
  
  伊藤光弘
- Project Period (FY)
  1992
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  代数学・幾何学
- Research Institution
  University of Tsukuba
環論とその関連分野の総合的研究
- Principal Investigator
  
  加藤豊紀
- Project Period (FY)
  1991
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  代数学・幾何学
- Research Institution
  University of Tsukuba
ホップ代数,代数群,量子群の表現とその応用Principal Investigator
- Principal Investigator
  
  竹内光弘
- Project Period (FY)
  1990
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  代数学・幾何学
- Research Institution
  University of Tsukuba
数論とその周辺分野における諸方法の綜合的研究
- Principal Investigator
  
  内山三郎
- Project Period (FY)
  1990
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  代数学・幾何学
- Research Institution
  University of Tsukuba
多元環の表現論とその関連分野の研究
- Principal Investigator
  
  太刀川弘幸
- Project Period (FY)
  1989
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  代数学・幾何学
- Research Institution
  University of Tsukuba
代数群、有限群の理論と関連分野への応用
- Principal Investigator
  
  阿部英一
- Project Period (FY)
  1988
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  代数学・幾何学
- Research Institution
  University of Tsukuba
群論及び関連する問題の研究
- Principal Investigator
  
  八牧宏美
- Project Period (FY)
  1986
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  代数学・幾何学
- Research Institution
  University of Tsukuba

All 2010 2009 2007

All Journal Article

[Journal Article] FRT construction for dynamical Yang-Baxter maps2010
- Author(s)
  Y.Shibukawa, M.Takeuchi
- Journal Title
  
  Journal of Algebra 323
  
  Pages: 1698-1728
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18540008
[Journal Article] FRT construction for dynamical Yang-Baxter maps2010
- Author(s)
  Y. Shibukawa, M. Takeuchi
- Journal Title
  
  Journal of Algebra Vol. 323
  
  Pages: 1698-1728
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18540008
[Journal Article] Hopf algebraic approach to Picard-Vessiot theory2009
- Author(s)
  K. Amano, A. Masuoka, M. Takeuchi
- Journal Title
  
  Handbook of Algebra Vol. 6
  
  Pages: 127-171
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18540008
[Journal Article] Hopf algebraic approach to Picard-Vessiot theory2009
- Author(s)
  K.Amano, A.Masuoka, M.Takeuchi
- Journal Title
  
  Handbook of Algebra Vol.6
  
  Pages: 127-171
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18540008
[Journal Article] Morita equivalences induced by bimodules over Hopf-Galois extensions2007
- Author(s)
  S.Caenepeel, S.Crivei, A.Marcus and M.Takeuchi
- Journal Title
  
  J. Algebra 314
  
  Pages: 267-302
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18540008
[Journal Article] Morita equivalences induced by bimodules over Hopf-Galois extensions2007
- Author(s)
  S. Caenepeel, S. Crivei, A. Marcus, M. Takeuchi
- Journal Title
  
  Journal of Algebra Vol. 314
  
  Pages: 267-302
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18540008
[Journal Article] Morita equivalences induced by bimodules over Hopf-Galois eztensions2007
- Author(s)
  S. Caenepeel, S. Crivei, A. Marcus and M. Takeuchi
- Journal Title
  
  Journal of Algebra 314
  
  Pages: 267-302
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18540008

1. MORITA Jun (20166416)

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2. KIMURA Tatsuo (30022726)

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3. MASUDA Tetsuya (70202314)

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4. YAMAGATA Kunio (60015849)

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5. YAMAKI Hiroyoshi (60028199)

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35. NISHIMURA Hirokazu (70135614)

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36. MIWA Tetsuji (10027386)

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37. SHOJI Toshiaki (40120191)

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38. KAJITANI Kunihiko (00026262)

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39. SAGAKI Daisuke (40344866)

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48. 山崎満 (30240732)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
49. 宮西正宣 (80025311)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
50. 堀田良之 (70028190)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
51. 日比孝之 (80181113)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
52. 兼田正治 (60204575)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
53. 木村弘信 (40161575)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
54. 坂井公 (20241797)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results

TAKEUCHI Mitsuhiro 竹内 光弘

竹内 光弘

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Hopf algebras and their applications to quantum groupsPrincipal Investigator

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Research on quantum matrices and Hopf algebrasPrincipal Investigator

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量子群とリー代数の表現論Principal Investigator

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TAKEUCHI Mitsuhiro 竹内光弘

竹内光弘