On sums of gr-PI algebras

Autor(es)

Fagundes, Pedro ; Koshlukov, Plamen

• Tipo de documento: Artigo Científico
• Fonte: Linear Algebra and its Applications; v. 677, p. 21-pg., 2023-08-28.

Resumo

Let A = B + C be an associative algebra graded by a group G, which is a sum of two homogeneous subalgebras B and C. We prove that if B is an ideal of A, and both B and C satisfy graded polynomials identities, then the same happens for the algebra A. We also introduce the notion of graded semi-identity for the algebra A graded by a finite group and we give sufficient conditions on such semi-identities in order to obtain the existence of graded identities on A. We also provide an example where both subalgebras B and C satisfy graded identities while A = B+C does not. Thus the theorem proved by K,epczyk in 2016 does not transfer to the case of group graded associative algebras. A variation of our example shows that a similar statement holds in the case of group graded Lie algebras. We note that there is no known analogue of K,epczyk's theorem for Lie algebras. (AU)

• Processo FAPESP: 22/05256-2 - Imagens de polinômios multilineares sobre UT_2 e UT_3 com involuções
• Beneficiário: Pedro Souza Fagundes
• Modalidade de apoio: Bolsas no Exterior - Estágio de Pesquisa - Doutorado
• Processo FAPESP: 19/16994-1 - Álgebras que são soma de duas subálgebras PI
• Beneficiário: Pedro Souza Fagundes
• Modalidade de apoio: Bolsas no Brasil - Doutorado
• Processo FAPESP: 18/23690-6 - Estruturas, representações e aplicações de sistemas algébricos
• Beneficiário: Ivan Chestakov
• Modalidade de apoio: Auxílio à Pesquisa - Temático