Finite-dimensional non-associative algebras and codimension growth

Autor(es)

Giambruno, Antonio ^[1] ; Shestakov, Ivan ^{[2, 3]} ; Zaicev, Mikhail ^[4]

Afiliação do(s) autor(es)

^[1] Univ Palermo, Dipartimento Matemat & Applicaz, I-90123 Palermo - Italy

^[2] Sobolev Inst Math, Novosibirsk 630090 - Russia

^[3] Univ Sao Paulo, Inst Matemat & Estat, BR-05315970 Sao Paulo - Brazil

^[4] Moscow MV Lomonosov State Univ, Fac Math & Mech, Dept Algebra, Moscow 119992 - Russia

• Tipo de documento: Artigo Científico
• Fonte: ADVANCES IN APPLIED MATHEMATICS; v. 47, n. 1, p. 125-139, JUL 2011.
• Citações Web of Science: 23

Resumo

Let A be a (non-necessarily associative) finite-dimensional algebra over a field of characteristic zero. A quantitative estimate of the polynomial identities satisfied by A is achieved through the study of the asymptotics of the sequence of codimensions of A. It is well known that for such an algebra this sequence is exponentially bounded. Here we capture the exponential rate of growth of the sequence of codimensions for several classes of algebras including simple algebras with a special non-degenerate form, finite-dimensional Jordan or alternative algebras and many more. In all cases such rate of growth is integer and is explicitly related to the dimension of a subalgebra of A. One of the main tools of independent interest is the construction in the free non-associative algebra of multialternating polynomials satisfying special properties. (C) 2010 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 05/60337-2 - Álgebras de Lie e de Jordan, suas representações e generalizações
• Beneficiário: Ivan Chestakov
• Modalidade de apoio: Auxílio à Pesquisa - Temático