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On associative representations of non-associative algebras

A. I. Kornev

Federal University of ABC (UFABC), Av. dos Estados, 5001-Bangú, Santo André-SP, 09210-580, Brazil

E-mail Address: alexandr.kornev@ufabc.edu.br

Corresponding author.

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and

I. P. Shestakov

University of São Paulo (USP), Butantã, São Paulo, State of São Paulo, 03178-200, Brazil

E-mail Address: shestak@ime.usp.br

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https://doi.org/10.1142/S0219498818500512Cited by:7 (Source: Crossref)

Abstract

We define a notion of associative representation for algebras. We prove the existence of faithful associative representations for any alternative, Mal’cev, and Poisson algebra, and prove analogs of Ado-Iwasawa theorem for each of these cases. We construct also an explicit associative representation of the Cayley–Dickson algebra in the matrix algebra $M_{8} (F) .$

Communicated by L. Bokut

Keywords:

AMSC: 17D01, 17D05, 17D10, 17D99

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