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Title
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Cocommutative Calabi-Yau Hopf algebras and deformations
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Author
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Abstract
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| 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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Language
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English
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Source (journal)
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Journal of algebra. - New York, N.Y., 1964, currens
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Publication
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New York, N.Y.
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Academic Press
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2010
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ISSN
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0021-8693
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DOI
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10.1016/J.JALGEBRA.2010.06.010
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Volume/pages
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324
:8
(2010)
, p. 1921-1939
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ISI
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000281976500008
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Full text (Publisher's DOI)
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