Title
Cocommutative Calabi-Yau Hopf algebras and deformationsCocommutative Calabi-Yau Hopf algebras and deformations
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Research group
Fundamental Mathematics
Publication type
article
Publication
New York, N.Y.,
Subject
Mathematics
Source (journal)
Journal of algebra. - New York, N.Y.
Volume/pages
324(2010):8, p. 1921-1939
ISSN
0021-8693
ISI
000281976500008
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
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.
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