Campus Units

Mathematics

Document Type

Article

Publication Version

Submitted Manuscript

Publication Date

2009

Journal or Book Title

Contemporary Mathematics

Volume

483

First Page

73

Last Page

89

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.

Comments

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." Contemporary Mathematics 483 (2009): 73-89. Posted with permission.

Rights

First published in Contemporary Mathematics in vol. 483, 2009, published by the American Mathematical Society.

Creative Commons License

Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

Copyright Owner

American Mathematical Society

Language

en

File Format

application/pdf

Included in

Algebra Commons

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