| Texto completo | |
| Autor(es): |
Centrone, Lucio
;
Koshlukov, Plamen
;
Pereira, Kaue
Número total de Autores: 3
|
| Tipo de documento: | Artigo Científico |
| Fonte: | Journal of Pure and Applied Algebra; v. 229, n. 6, p. 20-pg., 2025-06-01. |
| Resumo | |
Let A = A(1 )circle plus & ctdot;circle plus A(r) be a decomposition of the algebra A as a direct sum of vector subspaces. If for every choice of the indices 1 <= i(j )<= r there exist a(ij )is an element of A(ij) such that the product a(i1 )& ctdot;a(in )not equal 0, and for every 1 <= i, j <= r there is a constant beta(i, j) not equal 0 with a(i)a(j )= beta(i, j)a(j)a(i) for a(i )is an element of A(i), a(j )is an element of A(j), the above decomposition is regular. Bahturin and Regev raised the following conjecture: suppose that the regular decomposition comes from a group grading on A, and form the rxr matrix whose (i, j)th entry equals beta(i, j). Then this matrix is invertible if and only if the decomposition is minimal (that is one cannot get a regular decomposition of A by coarsening the decomposition). Aljadeff and David proved that the conjecture is true in the case the base field is of characteristic 0. We prove that the conjecture does not hold for algebras over fields of positive characteristic, by constructing algebras with minimal regular decompositions such that the associated matrix is singular.<br /> (c) 2025 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies. (AU) | |
| Processo FAPESP: | 23/01673-0 - Produto tensorial graduado e álgebras regulares |
| Beneficiário: | Kauê Orlando Pereira |
| 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 |