arXiv subjects

Micael Said Garcia

Publications and source records attributed to Micael Said Garcia.

2 recordsLinked to original sources

arXiv2026

On homogeneous involutions on matrix algebras

We study the homogeneous involutions on the full square matrices over an algebraically closed field endowed with a division grading with commutative support. We obtain the classification of the isomorphism and equivalence classes for the Pauli grading. We also investigate the homogeneous involutions on the full square matrices with entries in a finite-dimensional graded-division algebra over an algebraically closed field of characteristic not $2$ endowed with an arbitrary grading by an arbitrary group.

math.RA↗

arXiv2024

Graded polynomial identities of the infinite-dimensional upper triangular matrices over an arbitrary field

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.

math.RA↗