On ℤ<sub><i>n</i></sub>-graded identities of block-triangular matrices

Centrone, Lucio; Mello, Thiago Castilho de

doi:10.1080/03081087.2013.865733

Cited by 7 publications

(7 citation statements)

References 13 publications

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“…Remark 4.6. We recall that in [4] and [8], the authors conjecture that the graded monomial identities of M n (F ) follow from the graded identities of degree up to n. We observe that once this conjecture is true, the same holds for the (G, * )-identities of M n (F ).…”

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confidence: 82%

“…Subsequent to the pioneering work of Di-Vincenzo [6] about graded identities, many authors described the graded identities of M n (F ) and other different important algebras in different contexts [1], [2], [3], [7], [17], [8], [4] and [18]. Also, identities with involution for M n (F ) have been studied by some authors [12].…”

Section: Introductionmentioning

confidence: 99%

“…The main tool here is the use of generic matrices, and we use ideas similar to those in [1], [2], [4], [7], and [8].…”

Section: Introductionmentioning

confidence: 99%

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Graded polynomial identities for matrices with the transpose involution over an infinite field

Fonseca

Mello

2017

Communications in Algebra

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Let F be an infinite field, and let M n (F ) be the algebra of n × n matrices over F . Suppose that this algebra is equipped with an elementary grading whose neutral component coincides with the main diagonal. In this paper, we find a basis for the graded polynomial identities of M n (F ) with the transpose involution. Our results generalize for infinite fields of arbitrary characteristic previous results in the literature which were obtained for the field of complex numbers and for a particular class of elementary G-gradings.

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confidence: 82%

Section: Introductionmentioning

confidence: 99%

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Graded polynomial identities for matrices with the transpose involution over an infinite field

Fonseca

Mello

2017

Communications in Algebra

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“…We recall that block-triangular matrices play an important role in PI-theory, see, for instance, [20]. Their related graded PI-properties have been a subject of several recent studies, see [10,16,15,5,13,14,17], to cite only a few examples. The group gradings on the upper block-triangular matrices were computed in [33,6,35].…”

Section: Introductionmentioning

confidence: 99%

Gradings on the algebra of triangular matrices as a Lie algebra: revisited

Koshlukov,

Yasumura

2021

Preprint

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We investigate the group gradings on the algebra of upper triangular matrices over an arbitrary field, viewed as a Lie algebra. These results were obtained a few years early by the same authors. We provide streamlined proofs, and present a complete classification of isomorphism classes of the gradings. We also provide a classification of the practical isomorphism classes of the gradings, which is a better alternative way to consider these gradings up to being essentially the same object. Finally, we investigate in details the case where the characteristic of the base field is 2, a topic that was neglected in previous works.

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“…The classification of the elementary gradings on the upper block triangular matrices was studied in [1]. The graded polynomial identities for the elementary gradings on the upper block triangular matrices was dealt in [2,8]. Also, in [3] the authors addressed the question of when the knowledge of the graded polynomial identities for a certain grading on the upper block triangular matrices completely determines the grading.…”

Section: Introductionmentioning

confidence: 99%