Graded polynomial identities for the upper triangular matrix algebra over a finite field

Gonçalves, Dimas José; Riva, Evandro

doi:10.1016/j.jalgebra.2020.05.008

Cited by 5 publications

(3 citation statements)

References 11 publications

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“…An immediate computation shows that the following are graded identities for : where the variables are neutral ones, z , , are nonneutral variables, and . A complete description of the graded polynomial identities for elementary gradings on was given in [11] for infinite fields and in [21] for finite fields.…”

Section: Certain -Gradings Onmentioning

confidence: 99%

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Images of multilinear graded polynomials on upper triangular matrix algebras

Fagundes¹,

Koshlukov²

2022

Can. J. Math.-J. Can. Math.

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In this paper we study the images of multilinear graded polynomials on the graded algebra of upper triangular matrices U Tn. For positive integers q ≤ n, we classify these images on U Tn endowed with a particular elementary Zq-grading. As a consequence, we obtain the images of multilinear graded polynomials on U Tn with the natural Zn-grading. We apply this classification in order to give a new condition for a multilinear polynomial in terms of graded identities so that to obtain the traceless matrices in its image on the full matrix algebra. We also describe the images of multilinear polynomials on the graded algebras U T 2 and U T 3 , for arbitrary gradings. We finish the paper by proving a similar result for the graded Jordan algebra U J 2 , and also for U J 3 endowed with the natural elementary Z 3 -grading.

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Section: Certain -Gradings Onmentioning

confidence: 99%

“…where the variables y i are neutral ones, z, z 1 , z 2 are non neutral variables and deg(z 1 ) + deg(z 2 ) = 0. A complete description of the graded polynomial identities for elementary gradings on U T n was given in [10] for infinite fields and in [20] for finite fields.…”

mentioning

confidence: 99%

Images of multilinear graded polynomials on upper triangular matrix algebras

Fagundes¹,

Koshlukov²

2022

Can. J. Math.-J. Can. Math.

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show abstract

“…We investigate the polynomial identities in the graded sense. As an associative algebra, all gradings and graded polynomial identities were understood, see [3,7,17]. The characterization from [3] gave us the insight to deal with the Lie case.…”

Section: Introductionmentioning

confidence: 99%