Polynomial identities for the Jordan algebra of 2 × 2 upper triangular matrices

Gonçalves, Dimas José; Koshlukov, Plamen; Salomão, Mateus Eduardo

doi:10.1016/j.jalgebra.2021.11.020

Cited by 14 publications

(11 citation statements)

References 16 publications

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“…For the grading (II)(a), we recall a lemma from [22] applied to multilinear polynomials. In order to make the notation more compact, we omit the symbol ○ for the Jordan product, and we write ab instead of a ○ b.…”

Section: The Graded Jordan Algebra U Jmentioning

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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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: The Graded Jordan Algebra U Jmentioning

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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“…Then we make the following evaluation: Since char(F ) = 2 and α = 0, it follows that Im(f ) = A g . Now we consider the grading (II)(b) and we recall another lemma from [21].…”

Section: 2mentioning

confidence: 99%

“…Hence we define an order on words in even variables Y 1 < Y 2 considering the left lexicographic order in case Y 1 and Y 2 have the same length, and Y 1 < Y 2 in case Y 2 is longer than Y 1 . For the next lemma we use ideas from [21,Lemma 5.6]. We denote by T the T -ideal generated by the identities from Lemma 6.22.…”

mentioning

confidence: 99%

Images of multilinear graded polynomials on upper triangular matrix algebras

Fagundes,

Koshlukov

2022

Preprint

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“…Análise espectral singular 122,123,124,125,126,128,135 Anéis 89,91 Avaliação 1,2,3,4,5,6,7,8,9,10,31,117,130 B Backpropagation 190,191,197,198,199,202,205,206,207,209,216,238 Bifurcação 143,144,147,150,151,152 Bolsa de valores 190,193,195,196,197,198,199,200,201,240 C Cálculo 20,27,42,43,45,48,49,50,51,54,55,57,58,<...…”

Section: íNdice Remissivo Amentioning

confidence: 99%

A Álgebra De Jordan Das Matrizes Triangulares Superiores De Ordem 2 E Suas Identidades Polinomiais

Salomão¹

2022

Investigação Científica Em Matemática E Suas Aplicações

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Direitos para esta edição cedidos à Atena Editora pelos autores. Open access publication by Atena Editora Todo o conteúdo deste livro está licenciado sob uma Licença de Atribuição Creative Commons. Atribuição-Não-Comercial-NãoDerivativos 4.0 Internacional (CC BY-NC-ND 4.0). O conteúdo dos artigos e seus dados em sua forma, correção e confiabilidade são de responsabilidade exclusiva dos autores, inclusive não representam necessariamente a posição oficial da Atena Editora. Permitido o download da obra e o compartilhamento desde que sejam atribuídos créditos aos autores, mas sem a possibilidade de alterá-la de nenhuma forma ou utilizá-la para fins comerciais.Todos os manuscritos foram previamente submetidos à avaliação cega pelos pares, membros do Conselho Editorial desta Editora, tendo sido aprovados para a publicação com base em critérios de neutralidade e imparcialidade acadêmica.A Atena Editora é comprometida em garantir a integridade editorial em todas as etapas do processo de publicação, evitando plágio, dados ou resultados fraudulentos e impedindo que interesses financeiros comprometam os padrões éticos da publicação. Situações suspeitas de má conduta científica serão investigadas sob o mais alto padrão de rigor acadêmico e ético.

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Polynomial identities for the Jordan algebra of 2 × 2 upper triangular matrices

Cited by 14 publications

References 16 publications

Images of multilinear graded polynomials on upper triangular matrix algebras

Images of multilinear graded polynomials on upper triangular matrix algebras

Images of multilinear graded polynomials on upper triangular matrix algebras

A Álgebra De Jordan Das Matrizes Triangulares Superiores De Ordem 2 E Suas Identidades Polinomiais

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Polynomial identities for the Jordan algebra of 2 × 2 upper triangular matrices

Cited by 14 publications

References 16 publications

Images of multilinear graded polynomials on upper triangular matrix algebras

Images of multilinear graded polynomials on upper triangular matrix algebras

Images of multilinear graded polynomials on upper triangular matrix algebras

A Álgebra De Jordan Das Matrizes Triangulares Superiores De Ordem 2 E Suas Identidades Polinomiais

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Product

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Polynomial identities for the Jordan algebra of 2 × 2 upper triangular matrices