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Enveloping algebras of Malcev algebras

Murray R. BremnerIrvin R. HentzelLuiz A. PeresiMarina V. TvalavadzeHamid Usefi — 2010

Commentationes Mathematicae Universitatis Carolinae

We first discuss the construction by Pérez-Izquierdo and Shestakov of universal nonassociative enveloping algebras of Malcev algebras. We then describe recent results on explicit structure constants for the universal enveloping algebras (both nonassociative and alternative) of the 4-dimensional solvable Malcev algebra and the 5-dimensional nilpotent Malcev algebra. We include a proof (due to Shestakov) that the universal alternative enveloping algebra of the real 7-dimensional simple Malcev algebra...

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