| Full text | |
| Author(s): |
Correa, Daniela Martinez
;
Koshlukov, Plamen
Total Authors: 2
|
| Document type: | Journal article |
| Source: | MONATSHEFTE FUR MATHEMATIK; v. N/A, p. 28-pg., 2023-03-27. |
| Abstract | |
Let UTn(F) be the algebra of the nxn upper triangular matrices and denote UTn(F)((-)) the Lie algebra on the vector space of UTn(F) with respect to the usual bracket (commutator), over an infinite field F. In this paper, we give a positive answer to the Specht property for the ideal of the Z(n)-graded identities of UTn(F)((-)) with the canonical grading when the characteristic p of F is 0 or is larger than n-1. Namely we prove that every ideal of graded identities in the free graded Lie algebra that contains the graded identities of UTn(F)((-)), is finitely based. Moreover we show that if F is an infinite field of characteristic p = 2 then the Z(3)-graded identities of UT(-) (3) (F) do not satisfy the Specht property. More precisely, we construct explicitly an ideal of graded identities containing that of UT(-) (3) (F), and which is not finitely generated as an ideal of graded identities. (AU) | |
| FAPESP's process: | 18/23690-6 - Structures, representations, and applications of algebraic systems |
| Grantee: | Ivan Chestakov |
| Support Opportunities: | Research Projects - Thematic Grants |