Let F be a field of characteristic diferent from 2. Denote by UT2(F) the 2x2 upper triangular matrix F-algebra. If * is a involution of first kind of UT2(F), denote by Id(UT2(F); * and C(UT2(F); *) the set of its ...

Let F be an infinite field of characteristic different from 2. In this thesis we will study the polynomial identities and central polynomials with involution for two important classes of algebras. More precisely, we describe ...

In this thesis, the main object of study is the class of the (G, ∗)-algebras, that is, algebras graded by a group G and endowed with a graded involution ∗. Firstly, we study the algebraic structure of the (G, ∗)-algebras. ...

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 ...

Let $F$ be a field of characteristic zero. An associative superalgebra $A = A_{0} \oplus A_{1}$ endowed with an involution $\ast$ is a $\ast$-superalgebra if $A_{0}^{\ast} = A_{0}$ and $A_{1}^{\ast} = A_{1}$. In this case, ...

If A is a superalgebra endowed with a graded involution or asuperinvolution, we say that A is a ψ-algebra. In this thesis we work with unitary ψ-algebras whose ψ-codimension sequence cψn(A) is polynomially bounded. Under ...

Let F be a field of characteristic zero. Considering that the T-ideal of the algebra of matrices M3(F) is still unknown, some authors study such algebra endowed with additional structures. This thesis was inspired by the ...

Let V be a variety of superalgebras with graded involution and let $\{\cgri(v)\}_{n\geq 1}$ be its sequence of *-graded codimensions. We say that V has polynomial growth $n^k$ if asymptotically $\cgri(V)\approx an^k$, for ...

By a ϕ-variety V we mean a supervariety or a ∗-variety generated by an associative algebra over a field F of characteristic zero. In this case, we can consider its sequence of ϕ-codimensions cϕ n(V). We say that V is minimal ...