Identidades em variáveis simétricas para M2m(C) com involução simplética

Abstract

In this work we are interested in the studying lower and upper bounds for the degree of the polynomial identity in symmetric variables for the F-algebra M2m(F) endowed with the symplectic involution s (F a eld of characteristic 0). We will exhibit the proof of result given in [11], wich establishes that (M2m(F); s)+ satis es a multilinear identity of degree 4m 3 for m > 1 a positive integer and F a eld. We will also present the construction and the GAP implementation of a basis for the F-algebra M2m(C), wich is particularly interesting since their elements are invertible and each one of them is symmetric or skew with respect to the symplectic involution. We believe that exploring deeply the properties, of this basis we can use it to nd new identities for M2m(C) with involution s.