Universal enveloping algebras of the four-dimensional Malcev algebra

Date
2009-01-01
Authors
Bremner, Murray
Hentzel, Irvin
Hentzel, Irvin
Peresi, Luiz
Usefi, Hamid
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Abstract

We determine structure constants for the universal nonassociative enveloping algebra U(M) of the four-dimensional non-Lie Malcev algebra M by constructing a representation of U(M) by differential operators on the polynomial algebra P (M). These structure constants involve Stirling numbers of the second kind. This work is based on the recent theorem of Pérez-Izquierdo and Shestakov which generalizes the Poincaré-Birkhoff-Witt theorem from Lie algebras to Malcev algebras. We use our results for U(M) to determine structure constants for the universal alternative enveloping algebra A(M) = U(M)/I(M) where I(M) is the alternator ideal of U(M). The structure constants for A(M) were obtained earlier by Shestakov using different methods.

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<p>This article is published as Bremner, Murray R., Irvin R. Hentzel, Luiz A. Peresi, and Hamid Usefi. "Universal enveloping algebras of the four-dimensional Malcev algebra." <em>Contemporary Mathematics</em> 483 (2009): 73-89. Posted with permission.</p>
Keywords
structure constant, four-dimensional malcev algebra, differential operator, recent theorem, different method, malcev algebra, poincar birkhoff-witt theorem, polynomial algebra, second kind, alternator ideal, lie algebra, four-dimensional non-lie malcev algebra
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