Title




Cocommutative CalabiYau 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 ASGorenstein Hopf algebras. It is shown that the skewgroup 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 3dimensional CalabiYau Sridharan enveloping algebras. 


Language




English


Source (journal)




Journal of algebra.  New York, N.Y., 1964, currens


Publication




New York, N.Y.
:
Academic Press
,
2010


ISSN




00218693


DOI




10.1016/J.JALGEBRA.2010.06.010


Volume/pages




324
:8
(2010)
, p. 19211939


ISI




000281976500008


Full text (Publisher's DOI)





