Codimension growth of simple Jordan superalgebras

Autor(es)

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

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Inst Matemat & Estat, Rua Matao 1010, BR-05508090 Sao Paulo - Brazil

^[2] Sobolev Inst Math, 4 Acad Koptyug Ave, Novosibirsk 630090 - Russia

^[3] Moscow MV Lomonosov State Univ, Fac Math & Mech, Dept Algebra, Moscow 119992 - Russia

• Tipo de documento: Artigo Científico
• Fonte: Israel Journal of Mathematics; v. 245, n. 2 OCT 2021.
• Citações Web of Science: 0

Resumo

We study asymptotic behaviour of graded and non-graded codimensions of simple Jordan superalgebras over a field of characteristic zero. It is known that the PI-exponent of any finite-dimensional associative or Jordan or Lie algebra A is a non-negative integer less than or equal to the dimension of algebra A. Moreover, the PI-exponent is equal to the dimension if and only if A is simple provided that the base field is algebraically closed. In the present paper we prove that for a Jordan superalgebra P(t) = H(M-t divide t, trp) its non-graded and DOUBLE-STRUCK CAPITAL Z(2)-graded exponents are strictly less than dim P(t). In particular, exp P(2) is fractional. (AU)

• Processo FAPESP: 19/02510-2 - Identidades polinomiais e invariantes numéricos
• Beneficiário: Ivan Chestakov
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Internacional
• Processo FAPESP: 18/23690-6 - Estruturas, representações e aplicações de sistemas algébricos
• Beneficiário: Ivan Chestakov
• Modalidade de apoio: Auxílio à Pesquisa - Temático