`Mixed' Jordan-Lie Superalgebra

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dc.creatorRaptis, Ioannis
dc.date2001-10-25
dc.date2001-11-14
dc.date.accessioned2026-07-07T04:28:42Z
dc.date.available2026-07-07T04:28:42Z
dc.descriptionAn algebra A not encountered in either the usual algebraic varieties or supervarieties is introduced. A is a graded and deformed version of the quaternions, with structure similar to that of a Jordan-Lie superalgebra as defined by Okubo and Kamiya, but it is shown to be neither that of a purely associative Lie superalgebra, nor that of a purely antiassociative Jordan-Lie superalgebra. Rather, it exhibits a novel kind of associativity, here called `ordered graded associativity', that is somewhat `in between' pure associativity and pure antiassociativity. In addition to graded associativity, the generators of A obey graded commutation relations encountered in both the usual Lie superalgebras and in graded Jordan-Lie algebras. They also satisfy new graded Jacobi identities that combine characteristics of the Jacobis obeyed by the generators of ungraded Lie, graded Lie and graded Jordan-Lie algebras. Mainly due to these three features, A is called a `mixed' Jordan-Lie superalgebra. The present paper defines A and compares it with the Jordan-Lie superalgebra defined by Okubo and Kamiya.
dc.description17 pages
dc.identifierhttps://arxiv.org/abs/math-ph/0110030
dc.identifierhttp://arxiv.org/abs/math-ph/0110030
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/56887
dc.subjectMathematical Physics
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectHigh Energy Physics - Theory
dc.title`Mixed' Jordan-Lie Superalgebra
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