Quantum groupoids and dynamical categories

J. Donin; Aim Mudrov

doi:10.1016/j.jalgebra.2006.01.001

Quantum groupoids and dynamical categories

J. Donin, Aim Mudrov

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

In this paper we realize the dynamical categories introduced in our previous paper as categories of modules over bialgebroids; we study the bialgebroids arising in this way. We define quasitriangular structure on bialgebroids and present examples of quasitriangular bialgebroids related to the dynamical categories. We show that dynamical twists over an arbitrary base give rise to bialgebroid twists. We prove that the classical dynamical r-matrices over an arbitrary base manifold are in one-to-one correspondence with a special class of coboundary Lie bialgebroids.

Original language	English
Pages (from-to)	348-384
Number of pages	37
Journal	Journal of Algebra
Volume	296
Issue number	2
DOIs	https://doi.org/10.1016/j.jalgebra.2006.01.001
State	Published - 15 Feb 2006

Bibliographical note

Funding Information:
✩ This research is supported in part by the Israel Academy of Sciences grant No. 8007/99-03, the Emmy Noether Research Institute for Mathematics, the Minerva Foundation of Germany, the Excellency Center “Group Theoretic Methods in the study of Algebraic Varieties” of the Israel Science Foundation, the CRDF grant RUM1-2622-ST-04, and by the RFBR grant No. 03-01-00593. * Corresponding author. E-mail addresses: [email protected], [email protected] (A. Mudrov).

Funding

✩ This research is supported in part by the Israel Academy of Sciences grant No. 8007/99-03, the Emmy Noether Research Institute for Mathematics, the Minerva Foundation of Germany, the Excellency Center “Group Theoretic Methods in the study of Algebraic Varieties” of the Israel Science Foundation, the CRDF grant RUM1-2622-ST-04, and by the RFBR grant No. 03-01-00593. * Corresponding author. E-mail addresses: [email protected], [email protected] (A. Mudrov).

Funders	Funder number
Citrus Research and Development Foundation	RUM1-2622-ST-04
Academy of Leisure Sciences	8007/99-03
Russian Foundation for Basic Research	03-01-00593
Israel Science Foundation

Keywords

Bialgebroid
Dynamical Yang-Baxter equation
Dynamical category
Dynamical twist
Lie bialgebroid
Quantum groupoid

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10.1016/j.jalgebra.2006.01.001

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title = "Quantum groupoids and dynamical categories",

abstract = "In this paper we realize the dynamical categories introduced in our previous paper as categories of modules over bialgebroids; we study the bialgebroids arising in this way. We define quasitriangular structure on bialgebroids and present examples of quasitriangular bialgebroids related to the dynamical categories. We show that dynamical twists over an arbitrary base give rise to bialgebroid twists. We prove that the classical dynamical r-matrices over an arbitrary base manifold are in one-to-one correspondence with a special class of coboundary Lie bialgebroids.",

keywords = "Bialgebroid, Dynamical Yang-Baxter equation, Dynamical category, Dynamical twist, Lie bialgebroid, Quantum groupoid",

author = "J. Donin and Aim Mudrov",

note = "Funding Information: ✩ This research is supported in part by the Israel Academy of Sciences grant No. 8007/99-03, the Emmy Noether Research Institute for Mathematics, the Minerva Foundation of Germany, the Excellency Center “Group Theoretic Methods in the study of Algebraic Varieties” of the Israel Science Foundation, the CRDF grant RUM1-2622-ST-04, and by the RFBR grant No. 03-01-00593. * Corresponding author. E-mail addresses: [email protected], [email protected] (A. Mudrov).",

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Quantum groupoids and dynamical categories

Abstract

Bibliographical note

Funding

Keywords

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