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. 

Publication 



New York, N.Y. : 2010


ISSN 



00218693


Volume/pages 



324:8(2010), p. 19211939


ISI 



000281976500008


Full text (Publishers DOI) 


 
