BEZERRA JÚNIOR, C. F.; http://lattes.cnpq.br/4742599384020324; BEZERRA JÚNIOR, Claudemir Fidelis.
Resumen:
In this dissertation we describe basis for the polynomial identities and central
polynomials with involution for the algebra of 2 × 2 matrices over an infinite field K
of characteristic p 6= 2 considering the transpose involution, denoted by t, and also
the symplectic involution, denoted by s. It is known that, since the field K is infinite,
if ∗ is an involution on M2(K), then the ideal of identities (M2(K), ∗) coincides with
(M2(K), t) or with (M2(K), s). We also consider the algebras Mn(E), Mk,l(E) and
M1,1(E) over fields of characteristic 0. For the algebras Mn(E) and Mk,l(E) we prove
that for a large class of involutions the polynomial identities with involution coincide
with the ordinary identities, and for the algebra M1,1(E) with the involution ∗ induced
by the transposition superinvolution of the superalgebra M1,1(K) we exhibit nite basis
for the ∗-polynomial identities.
