Graded Lie algebras defined by Jordan algebras and their representations

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dc.creatorKantor, Issai
dc.creatorShpiz, Gregory
dc.date2004-12-09
dc.date2004-12-10
dc.date.accessioned2026-07-07T05:15:08Z
dc.date.available2026-07-07T05:15:08Z
dc.descriptionWe introduce the notion of a generalized representation of a Jordan algebra with unit. The greneralized representation has the following properties: (1) Usual representations and Jacobson representations correspond to special cases of generalized representations. (2) Every simple Jordan algebra has infinitely many nonequivalent generalized representations. (3) There is a one-to-one correspondence between irreducible generalized representations of a Jordan algebra A and irreducible representations of a graded Lie algebra L(A)=U_{-1}\oplus U_0\oplus U_1 corresponding to A (the Lie algebra L(A) coincides with the TKK construction when A has a unit). The latter correspondence allows to use the theory of representations of Lie algebras to study generalized representations of Jordan algebras. In particular, one can classify irreducible generalized representations of semisimple Jordan algebras and also obtain classical results about usual representations and Jacobson representations in a simple way.
dc.description7 pages; MSC numbers updated
dc.identifierhttps://arxiv.org/abs/math/0412186
dc.identifierhttp://arxiv.org/abs/math/0412186
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/73536
dc.subjectRepresentation Theory
dc.subject17B60 (Primary) 16W10, 17B10, 17B70 (Secondary)
dc.titleGraded Lie algebras defined by Jordan algebras and their representations
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