Publication
Title
Cocommutative Calabi-Yau Hopf algebras and deformations
Author
Abstract
The CalabiYau 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 View the MathML source with a finite subgroup G of automorphisms of View the MathML source is CalabiYau if and only if the universal enveloping algebra itself is CalabiYau and G is a subgroup of the special linear group View the MathML source. The Noetherian cocommutative CalabiYau Hopf algebras of dimension not larger than 3 are described. The CalabiYau 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 CalabiYau, and then partly answer a question proposed by Berger. We list all the nonisomorphic 3-dimensional CalabiYau Sridharan enveloping algebras.
Language
English
Source (journal)
Journal of algebra. - New York, N.Y.
Publication
New York, N.Y. : 2010
ISSN
0021-8693
Volume/pages
324:8(2010), p. 1921-1939
ISI
000281976500008
Full text (Publishers DOI)
UAntwerpen
Faculty/Department
Research group
Publication type
Subject
Affiliation
Publications with a UAntwerp address
External links
Web of Science
Record
Identification
Creation 12.01.2011
Last edited 08.04.2017
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