Special Lie superalgebras with maximality condition for subalgebras |
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| Authors: | Oksana Bezushchak Mikhail Zaicev |
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| Institution: | 1. Department of Algebra, Faculty of Mathematics and Mechanics, Kiev National University, 2, Academician Glushkov Avenue, Building 7, Kiev, Ukraine
2. Department of Algebra, Faculty of Mathematics and Mechanics, Moscow State University, Moscow, 119992, Russia
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| Abstract: | We consider finitely generated Lie superalgebras over a field of characteristic zero satisfying Capelli identities. We prove that any such an algebra with the maximality condition for abelian subalgebras is finite dimensional. In particular, any special Lie superalgebra with the maximality condition for its subalgebras has a finite dimension. We also prove that the universal enveloping algebra U(L) of special Lie superalgebra L is Noetherian if and only if $\dim L<\infty$ . |
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