Specht property for some varieties of Jordan algebras of almost polynomial growth

Centrone, Lucio; Martino, Fabrizio; Souza, Manuela da Silva

doi:10.1016/j.jalgebra.2018.11.017

Cited by 15 publications

(7 citation statements)

References 19 publications

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“…We already have the key ingredients to prove the main result of this section. We want to highlight that we are going to use the algorithm described in full details in the paper [13].…”

Section: Andmentioning

confidence: 99%

Specht property for the algebra of upper triangular matrices of size two with a Taft’s algebra action

Centrone

Estrada²

2022

Can. Math. Bull.

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Let F be a field of characteristic zero, and let $UT_2$ be the algebra of $2 \times 2$ upper triangular matrices over F. In a previous paper by Centrone and Yasumura, the authors give a description of the action of Taft’s algebras $H_m$ on $UT_2$ and its $H_m$ -identities. In this paper, we give a complete description of the space of multilinear $H_m$ -identities in the language of Young diagrams through the representation theory of the hyperoctahedral group. We finally prove that the variety of $H_m$ -module algebras generated by $UT_2$ has the Specht property, i.e., every $T^{H_m}$ -ideal containing the $H_m$ -identities of $UT_2$ is finitely based.

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“…We already have the key ingredients to prove the main result of this section. We want to highlight that we are going to use the algorithm described in full details in the paper [13].…”

Section: Andmentioning

confidence: 99%

Specht property for the algebra of upper triangular matrices of size two with a Taft’s algebra action

Centrone

Estrada²

2022

Can. Math. Bull.

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“…Its polynomial identities, even the ordinary ones, are known only for triangular matrices of size 2 [9,8]. Moreover the Specht property for the corresponding ideals of graded identities is obtained for the same algebra of size 2, for all gradings [2]. Thus for the Jordan case, which is otherwise natural, we have much less information about its polynomial identities.…”

Section: Introductionmentioning

confidence: 99%

Graded polynomial identities for the Lie algebra of upper triangular matrices of order 3

Yasumura¹

2022

Preprint

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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. In [19] the graded identities for any Z 2 -grading on the Jordan algebra of symmetric matrices of order two were obtained, and in [29] the Specht property for the finite dimensional Jordan algebra of a non-degenerate symmetric bilinear form, graded by Z 2 , in characteristic 0, was established.…”

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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Specht property for some varieties of Jordan algebras of almost polynomial growth

Cited by 15 publications

References 19 publications

Specht property for the algebra of upper triangular matrices of size two with a Taft’s algebra action

Specht property for the algebra of upper triangular matrices of size two with a Taft’s algebra action

Graded polynomial identities for the Lie algebra of upper triangular matrices of order 3

Specht property of varieties of graded Lie algebras

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