This article is cited in 3 papers

The Variety of Jordan Algebras Determined by the Identity $(xy)(zt)\equiv0$ Has Almost Polynomial Growth

S. P. Mishchenko, A. V. Popov

Ulyanovsk State University

Abstract: We prove that, in the case of ground field of characteristic zero, the variety cited in the title has almost polynomial growth. We construct an algebra generating this variety and completely describe the structure of the multilinear part of the variety as a module of the symmetric group.

Keywords: variety of algebras, linear algebra over a field, Jordan algebra, growth of an algebra, symmetric group, polynomial identity, irreducible representation, Young diagram.

UDC: 512.572

Received: 29.06.2009
Revised: 09.10.2009

DOI: 10.4213/mzm8733

 English version: Mathematical Notes, 2010, 87:6, 854–859

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