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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/11307

Title: Cocommutative Calabi-Yau Hopf algebras and deformations
Authors: He, Ji-Wei
Van Oystaeyen, Fred
ZHANG, Yinhuo
Issue Date: 2010
Citation: JOURNAL OF ALGEBRA, 324(8). p. 1921-1939
Abstract: The Calabi-Yau property of cocommutative Hopf algebras is discussed by using the homological integral, a recently introduced tool for studying infinite dimensional AS-Gorenstein Hopf algebras. It is shown that the skew-group algebra of a universal enveloping algebra of a finite dimensional Lie algebra g with a finite subgroup G of automorphisms of g is Calabi-Yau if and only if the universal enveloping algebra itself is Calabi-Yau and G is a subgroup of the special linear group SL(g). The Noetherian cocommutative Calabi-Yau Hopi algebras of dimension not larger than 3 are described. The Calabi-Yau property of Sridharan enveloping algebras of finite dimensional Lie algebras is also discussed. We obtain some equivalent conditions for a Sridharan enveloping algebra to be Calabi-Yau. and then partly answer a question proposed by Berger. We list all the nonisomorphic 3-dimensional Calabi-Yau Sridharan enveloping algebras. (C) 2010 Elsevier Inc. All rights reserved.
Notes: [He, Ji-Wei; Van Oystaeyen, Fred] Univ Antwerp, Dept Math & Comp Sci, B-2020 Antwerp, Belgium. [He, Ji-Wei] Shaoxing Coll Arts & Sci, Dept Math, Shaoxing 312000, Zhejiang, Peoples R China. [Zhang, Yinhuo] Univ Hasselt, Dept WNI, B-3590 Diepenbeek, Belgium. jwhe@usx.edu.cn; fred.vanoystaeyen@ua.ac.be; yinhuo.zhang@uhasselt.be
URI: http://hdl.handle.net/1942/11307
DOI: 10.1016/j.jalgebra.2010.06.010
ISI #: 000281976500008
ISSN: 0021-8693
Category: A1
Type: Journal Contribution
Validation: ecoom, 2011
Appears in Collections: Research publications

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