The invariant polynomials on simple Lie superalgebras

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dc.creatorSergeev, Alexander
dc.date1998-10-17
dc.date.accessioned2026-07-07T05:26:31Z
dc.date.available2026-07-07T05:26:31Z
dc.descriptionChevalley's theorem states that for any simple finite dimensional Lie algebra G (1) the restriction homomorphism of the algebra of polynomials on G onto the Cartan subalgebra H induces an isomorphism between the algebra of G-invariant polynomials on G with the algebra of W-invariant polynomals on H, where W is the Weyl group of G, (2) each G-invariant polynomial is a linear combination of the powers of traces tr r(x), where r is a finite dimensional representation of G. None of these facts is necessarily true for simple Lie superalgebras. We reformulate Chevalley's theorem so as to embrace Lie superalgebras. Chevalley's theorem for anti-invariant polynomials is also given.
dc.description28 p., Latex
dc.identifierhttps://arxiv.org/abs/math/9810111
dc.identifierhttp://arxiv.org/abs/math/9810111
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/77576
dc.subjectRepresentation Theory
dc.subjectCommutative Algebra
dc.subject17A70 (Primary) 17B35, 13A50 (Secondary)
dc.titleThe invariant polynomials on simple Lie superalgebras
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