On the Ghost Centre of Lie Superalgebras

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dc.creatorGorelik, Maria
dc.date1999-10-21
dc.date.accessioned2026-07-07T05:31:15Z
dc.date.available2026-07-07T05:31:15Z
dc.descriptionWe define a notion of ghost centre of a Lie superalgebra g=g_0+g_1 which is a sum of invariants with respect to the usual adjoint action (centre) and invariants with respect to a twisted adjoint action (``anticentre''). We calculate the anticentre in the case when the top external degree of g_1 is a trivial g_0-module. We describe the Harish-Chandra projection of the ghost centre for basic classical Lie superalgebras and show that for these cases the ghost centre coincides with the centralizer of the even part of the enveloping algebra. The ghost centre of a Lie superalgebra plays a role of the usual centre of a Lie algebra in some problems of representation theory. For instance, for osp(1,2l) the annihilator of a Verma module is generated by the intersection with the ghost centre.
dc.description17 pages
dc.identifierhttps://arxiv.org/abs/math/9910114
dc.identifierhttp://arxiv.org/abs/math/9910114
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/79271
dc.subjectRepresentation Theory
dc.subject17B10; 17B35
dc.titleOn the Ghost Centre of Lie Superalgebras
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