Israel Journal of Mathematics

, Volume 188, Issue 1, pp 441–462 | Cite as

On ℤ2-graded identities of the super tensor product of UT 2(F) by the Grassmann algebra

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Abstract

Let F be a field of characteristic zero and E be the unitary Grassmann algebra generated over an infinite-dimensional F-vector space L. Denote by \(\mathcal{E} = \mathcal{E}^{(0)} \oplus \mathcal{E}^{(1)}\) an arbitrary ℤ2-grading of E such that the subspace L is homogeneous. Given a superalgebra A = A (0) ⊕ A (1), define the superalgebra \(A\hat \otimes \mathcal{E}\) by \(A\hat \otimes \mathcal{E} = (A^{(0)} \otimes \mathcal{E}^{(0)} ) \oplus (A^{(1)} \otimes \mathcal{E}^{(1)} )\). Note that when E is the canonical grading of E then \(A\hat \otimes \mathcal{E}\) is the Grassmann envelope of A. In this work we find bases of ℤ2-graded identities and we describe the ℤ2-graded codimension and cocharacter sequences for the superalgebras \(UT_2 (F)\hat \otimes \mathcal{E}\), when the algebra UT 2(F) of 2 ×2 upper triangular matrices over F is endowed with its canonical grading.

Keywords

Associative Algebra Irreducible Character Polynomial Identity Triangular Matrice Grassmann Algebra 
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Copyright information

© Hebrew University Magnes Press 2011

Authors and Affiliations

  1. 1.Departamento de MatemáticaInstituto de Ciências Exatas Universidade Federal de Minas GeraisBelo HorizonteBrasil

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