On the nilpotency degree of the algebra with identity x(n)=0

Autor(es)

Lopatin, Artem A. ^[1]

Afiliação do(s) autor(es)

^[1] SB RAS, Sobolev Inst Math, Omsk Branch, Fed State Budgetary Estab, Omsk 644099 - Russia

• Tipo de documento: Artigo Científico
• Fonte: Journal of Algebra; v. 371, p. 350-366, DEC 1 2012.
• Citações Web of Science: 4

Resumo

Denote by C-n,C-d the nilpotency degree of a relatively free algebra generated by d elements and satisfying the identity x(n) = 0. Under assumption that the characteristic p of the base field is greater than n/2, it is shown that C-n,C-d < n(log2(3d+2)+1) and C-n,C-d < 4. 2(n/2)d. In particular, it is established that the nilpotency degree C-n,C-d has a polynomial growth in case the number of generators d is fixed and p > n/2. For p not equal 2 the nilpotency degree C-4,C-d is described with deviation 3 for all d. As an application, a finite generating set for the algebra R-GL(n) of GL(n)-invariants of d matrices is established in terms of C-n,C-d. Several conjectures are formulated. (C) 2012 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 11/51047-1 - Artem Lopatin | Omsk Branch of Institute of Mathematics - Rússia
• Beneficiário: Ivan Chestakov
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Internacional