\ℤ₂-graded polynomial identities for the Jordan algebra of\n 2\× 2 upper triangular matrices

2020/11/22 by Dimas José Gonçalves, Gonçalves, Dimas J., Mateus Eduardo Salomão +1
Biochemistry, Genetics and Molecular Biology · Engineering · Mathematics · #16R10 #17C05 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Optical Network Technologies #Rings and Algebras (math.RA) #Sphingolipid Metabolism and Signaling

paper · pdf · doi:10.48550/arxiv.2011.11116

openalex publication_date 2020/11/22 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

Let K be a field (finite or infinite) of char(K)\≠ 2 and let\nUT_n=UT_n(K) be the n\× n upper triangular matrix algebra over K. If\n\⋅ is the usual product on UT_n then with the new product a\∘\nb=(1/2)(a\⋅ b +b\⋅ a) we have that UT_n is a Jordan algebra, denoted\nby UJ_n=UJ_n(K). In this paper, we describe the set of all\n\ℤ₂-graded polynomial identities of UJ₂ with any nontrivial\n\ℤ₂-grading. Moreover, we describe a linear basis for the\ncorresponding relatively free \ℤ₂-graded algebra.\n

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