Graded polynomial identities of the infinite-dimensional upper triangular matrices over an arbitrary field
Rings and Algebras
2024-02-19 v1
Abstract
We compute the graded polynomial identities of the infinite dimensional upper triangular matrix algebra over an arbitrary field. If the grading group is finite, we prove that the set of graded polynomial identities admits a finite basis. We find conditions under which a grading on such an algebra satisfies a nontrivial graded polynomial identity. Finally, we provide examples showing that two nonisomorphic gradings can have the same set of graded polynomial identities.
Cite
@article{arxiv.2402.10839,
title = {Graded polynomial identities of the infinite-dimensional upper triangular matrices over an arbitrary field},
author = {Micael Said Garcia and Felipe Yukihide Yasumura},
journal= {arXiv preprint arXiv:2402.10839},
year = {2024}
}