Cocharacters and gradedGelfand-Kirillov dimension for PI-algebras
Representations of non-associative algebras and superalgebras
Images of polynomials on superalgebras and commutators on algebras
| Full text | |
| Author(s): |
de Mello, Thiago Castilho
Total Authors: 1
|
| Document type: | Journal article |
| Source: | ARCHIV DER MATHEMATIK; v. 118, n. 4, p. 10-pg., 2022-03-10. |
| Abstract | |
Let K be a field of characteristic different from 2 and let G be a group. If the algebra UTn of n x n upper triangular matrices over K is endowed with a G-grading Gamma : UTn = circle plus(g is an element of G)A(g), we give necessary and sufficient conditions on G that guarantees the existence of a homogeneous antiautomorphism on A, i.e., an antiautomorphism. satisfying phi(A(g)) = A(theta(g)) for some permutation theta of the support of the grading. It turns out that UTn admits a homogeneous antiautomorphism if and only if the reflection involution of UTn is homogeneous. Moreover, we prove that if one homogeneous antiautomorphism of UTn is defined by the map theta, then any other homogeneous antiautomorphism is defined by the same map theta. (AU) | |
| FAPESP's process: | 18/23690-6 - Structures, representations, and applications of algebraic systems |
| Grantee: | Ivan Chestakov |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 18/15627-2 - Gradings, automorphisms and identities in algebras |
| Grantee: | Thiago Castilho de Mello |
| Support Opportunities: | Regular Research Grants |