Search results for "polynomial identitiy"

On the asymptotics for $ast$-Capelli identities

Let Fbe the free associative algebra with involution ∗ over a field of characteristic zero. If L and M are two natural numbers let Γ∗_M+1,L+1 denote theT∗-idealofFgenerated by the∗-capellipolynomialsCap+M+1,Cap−L+1 alternanting on M+1 symmetric variables and L+1skew variables,respectively.It is well known that, if F is an algebraic closed field, every finite dimensional ∗-simple algebra is isomorphic to one of the following algebras (see [4], [2]):· (Mk(F),t) with the transpose involution; · (M2m(F),s) with the symplectic involution; · (Mk(F)⊕Mk(F)op,∗) with the exchange involution. The aim of this talk is to show a relation among the asymptotics of the∗-codimensions of the finite dimensional ∗…