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Cocommutative Calabi–Yau Hopf algebras and deformations by Ji-Wei He; Fred Van Oystaeyen; Yinhuo Zhang is a Mathematics article available to read on EtoBox.

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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 Hopf 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.

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Author

Ji-Wei He; Fred Van Oystaeyen; Yinhuo Zhang

Publisher

Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0021-8693)

Published

2010

Language

EN

Field

Mathematics (Physical Sciences)