The centre of generic algebras of small PI algebras

Autor(es)

Koshlukov, Plamen ^[1] ; de Mello, Thiago Castilho ^[1]

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, Dept Math, IMECC, BR-13083859 Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Algebra; v. 375, p. 109-120, FEB 1 2013.
• Citações Web of Science: 1

Resumo

Verbally prime algebras are important in PI theory. They are well known over a field K of characteristic zero: 0 and K < T > (the trivial ones), M-n(K), M-n(E), M-ab(E). Here K < T > is the free associative algebra with free generators T, E is the infinite dimensional Grassmann algebra over K. M-n(K) and M-n(E) are the n x n matrices over K and over E, respectively. Moreover M-ab(E) are certain subalgebras of Ma+b(E), defined below. The generic algebras of these algebras have been studied extensively. Procesi gave a very tight description of the generic algebra of M-n(K). The situation is rather unclear for the remaining nontrivial verbally prime algebras. In this paper we study the centre of the generic algebra of M-11 (E) in two generators. We prove that this centre is a direct sum of the field and a nilpotent ideal (of the generic algebra). We describe the centre of this algebra. As a corollary we obtain that this centre contains nonscalar elements thus we answer a question posed by Berele. (C) 2012 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 10/50347-9 - Álgebras, representações e aplicações
• Beneficiário: Ivan Chestakov
• Modalidade de apoio: Auxílio à Pesquisa - Temático