Related papers: Graded polynomial identities for matrices with the…

We show that unital simple C*-algebras with tracial topological rank zero which are locally approximated by subhomogeneous C^-algebras can be classified by their ordered $K$-theory. We apply this classification result to show that certain…

We examine crossed product C*-algebras associated with non-minimal free actions of countably infinite discrete abelian groups on the circle, extending the work of Putnam, Schmidt, and Skau. We obtain a large class of unital separable…

We study identities of finite dimensional algebras over a field of characteristic zero, graded by an arbitrary groupoid $\Gamma$. First we prove that its graded colength has a polynomially bounded growth. For any graded simple algebra $A$…

Let $\mathbb{F}$ be a field and let $M_2(\mathbb{F})$ be the algebra of $2\times 2$ matrices endowed with an involution of the first kind. We study the image of multilinear $*$-polynomials evaluated on $M_2(\mathbb{F})$. For the transpose…

The toric fiber product is a general procedure for gluing two ideals, homogeneous with respect to the same multigrading, to produce a new homogeneous ideal. Toric fiber products generalize familiar constructions in commutative algebra like…

The algebra of $n\times n$ matrices over a field $F$ has a natural $\mathbb{Z}_n$-grading. Its graded identities have been described by Vasilovsky who extended a previous work of Di Vincenzo for the algebra of $2\times 2$ matrices. In this…

We obtain a Galois correspondence between the lattice of intermediate C*-discrete subalgebras intermediate to a given irreducible C*-discrete inclusion, and characterize these as targets of compatible expectations under a traciality…

We describe the $C^*$-algebra of an $E$-unitary or strongly 0-$E$-unitary inverse semigroup as the partial crossed product of a commutative $C^*$-algebra by the maximal group image of the inverse semigroup. We give a similar result for the…

Let G be a group and A be a G-graded algebra satisfying a polynomial identity. We buid up a model for the relative free G-graded algebra and we obtain, as an application, the "factoring" property for the T_G-ideals of block triangular…

The paper presents a construction of the crossed product of a C*-algebra by a commutative semigroup of bounded positive linear maps generated by partial isometries. In particular, it generalizes Antonevich, Bakhtin, Lebedev's crossed…

The M-polynomial provides a unifying framework for a wide class of degree-based topological indices. Despite its structural importance, general methods for computing the M-polynomial under graph constructions remain limited. In this paper,…

We investigate the representation theory of the crossed-product C*-algebra associated to a compact group G acting on a locally compact space X when the stability subgroups vary discontinuously. Our main result applies when G has a principal…

We study the algebra of upper triangular matrices endowed with a group grading and a homogeneous involution over an infinite field. We compute the asymptotic behaviour of its (graded) star-codimension sequence. It turns out that the…

The symmetries described by Pin groups are the result of combining a finite number of discrete reflections in (hyper)planes. The current work shows how an analysis using geometric algebra provides a picture complementary to that of the…

We prove that an isomorphism of graded Grothendieck groups $K^{gr}_0$ of two Leavitt path algebras induces an isomorphism of a certain quotient of algebraic filtered $K$-theory and consequently an isomorphism of filtered $K$-theory of their…

Graph independence (also known as $\epsilon$-independence or $\lambda$-independence) is a mixture of classical independence and free independence corresponding to graph products or groups and operator algebras. Using conjugation by certain…

A Mauldin-Williams graph $\mathcal{M}$ is a generalization of an iterated function system by a directed graph. Its invariant set $K$ plays the role of the self-similar set. We associate a $C^{*}$-algebra $\mathcal{O}_{\mathcal{M}}(K)$ with…

This paper is devoted to the study of graded associative algebras that satisfy a graded polynomial identity of degree $2$. % Let $\mathsf{G}$ be a finite abelian group, $\mathbb{F}$ a field of characteristic zero and $\mathfrak{A}$ a…

We systematically develop a theory of graded semigroups, that is semigroups S partitioned by groups G, in a manner compatible with the multiplication on S. We define a smash product S#G, and show that when S has local units, the category…

Let $F$ be an algebraically closed field of characteristic zero, and $G$ be a finite abelian group. If $A=\oplus_{g\in G} A_g$ is a $G$-graded algebra, we study degree-inverting involutions on $A$, i.e., involutions $*$ on $A$ satisfying…