Actions of Lie Superalgebras on Reduced Rings |
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Authors: | Jeffrey Bergen Piotr Grzeszczuk Małgorzata Hryniewicka |
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Affiliation: | (1) Department of Mathematics, DePaul University, 2320 N. Kenmore Avenue, Chicago, IL 60614, USA;(2) Faculty of Computer Science, Technical University of Białystok, Wiejska 45A, 15-351 Białystok, Poland;(3) Institute of Mathematics, University of Białystok, Akademicka 2, 15-267 Białystok, Poland |
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Abstract: | In this paper, we look at the question of whether the subring of invariants is always nontrivial when a finite dimensional Hopf algebra acts on a reduced ring. Affirmative answers where given by Kharchenko for group algebras and by Beidar and Grzeszczuk for finite dimensional restricted Lie algebras. Our main result is Theorem 13 If R is a graded-reduced ring of characteristic p > 2 acted on by a finitely generated restricted K-Lie superalgebra L, then . We can then use Theorem 13 to prove Corollary 15 Let R be a reduced algebra over a field K of characteristic p > 2 acted on by a finite dimensional restricted K-Lie superalgebra L and let H = u(L)#G, where G is the group of order 2 with the natural action on L. If R H satisfies a polynomial identity of degree d, then R satisfies a polynomial identity of degree dN, where N is the dimension of H. Presented by Donald S. Passman. |
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Keywords: | Lie superalgebra Reduced ring Subring of invariants |
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