A note on cocharacter sequence of Jordan upper triangular matrix algebra

Centrone, Lucio; Martino, Fabrizio

doi:10.1080/00927872.2016.1222408

Cited by 14 publications

(4 citation statements)

References 8 publications

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“…The variety generated by U J 2 = U J 2 (F ) was extensively studied in the past years. For instance, in [1,3,18] a basis for the graded identities, the corresponding cocharacter sequence and the Gelfand-Kirillov dimension were found. Moreover, in [2] it was proved that var(U J 2 ), endowed with any grading, has the Specht property, i.e.…”

Section: The Variety Generated By U J 2 (F )mentioning

confidence: 99%

Varieties of special Jordan algebras of almost polynomial growth

Martino

2019

Journal of Algebra

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Section: The Variety Generated By U J 2 (F )mentioning

confidence: 99%

Varieties of special Jordan algebras of almost polynomial growth

Martino

2019

Journal of Algebra

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“…In [18] and [3] the authors studied graded identities for U J 2 , the Jordan algebra of 2 ˆ2 upper triangular matrices. In [4] it was shown that the variety generated by U J 2 has the Specht property when it is graded by any finite abelian group.…”

Section: Introductionmentioning

confidence: 99%

Specht property of varieties of graded Lie algebras

Correa¹,

Koshlukov²

2022

Preprint

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Let U TnpF q be the algebra of the n ˆn upper triangular matrices and denote U TnpF q p´q the Lie algebra on the vector space of U TnpF q 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 Zn-graded identities of U TnpF q p´q 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 U TnpF q p´q , is finitely based.Moreover we show that if F is an infinite field of characteristic p " 2 then the Z 3 -graded identities of U T p´q 3 pF q do not satisfy the Specht property. More precisely, we construct explicitly an ideal of graded identities containing that of U T p´q 3 pF q, and which is not finitely generated as an ideal of graded identities.

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“…Meanwhile, several authors were interested in the study of (graded) PI-related properties of the algebra of 2 × 2 upper triangular matrices viewed as a Jordan algebra [8,9,11]. Also, recent works were dedicated to investigating the same algebra over finite fields [21], and over fields of characteristic 2 [29].…”

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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A note on cocharacter sequence of Jordan upper triangular matrix algebra

Cited by 14 publications

References 8 publications

Varieties of special Jordan algebras of almost polynomial growth

Varieties of special Jordan algebras of almost polynomial growth

Specht property of varieties of graded Lie algebras

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

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