The graded identities of upper triangular matrices of size two

By Angela Valenti. 2002

49 citations recorded by the source corpus.

Let UT2 be the algebra of 2 × 2 upper triangular matrices over a 0eld F. We 0rst classify all possible gradings on UT2 by a group G. It turns out that, up to isomorphism, there is only one non-trivial grading and we study all the graded polynomial identities for such algebra. In case F is of characteristic zero we give a complete description of the space of multilinear graded identities in the language of Young diagrams through the representation theory of the hyperoctahedral group. We 0nally establish a result concerning the rate of growth of the identities for such algebra by proving that its sequence of graded codimensions has almost polynomial growth. c

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

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