Related papers: Essential dimension and error-correcting codes

We explore the concept of additive diameters in the context of group representations, unifying various noncommutative Waring-type problems. Given a finite-dimensional representation $\rho \colon G \to \mathrm{GL}(V)$ and a subspace $U \leq…

Let $G$ be a finite classical group of Lie type of rank $\ell$, defined over a field of characteristic $p>2$. In this work, we classify the irreducible representations of $G$ whose dimensions are bounded by a constant proportional to…

Let $F$ be a field of characteristic zero and let $ \mathcal V $ be a variety of associative $F$-algebras graded by a finite abelian group $G$. To a variety $ \mathcal V $ is associated a numerical sequence called the sequence of proper…

In this paper, we investigate, for varieties over $\mathbb C$ with trivial group of $0$-cycles, the gap between essential $\mathrm{CH}_0$-dimension $2$ and essential $\mathrm{CH}_0$-dimension $0$. In particular, we present sufficient (and…

Let $R$ be an associative ring with 1, $G=GL(n, R)$ be the general linear group of degree $n\ge 3$ over $R$. In this paper we calculate the relative centralisers of the relative elementary subgroups or the principal congruence subgroups,…

The study of different types of ideals in non self-adjoint operator algebras has been a topic of recent research. This study focuses on principal ideals in subalgebras of groupoid C*-algebras. An ideal is said to be principal if it is…

In recent years, the study of the $T$-space of central polynomials of an algebra $A$ has become an object of great interest in the PI-theory. Such interest has been extended to the context of algebras with additional structures. The main…

The classification of the finite subgroups of $\mathrm{GL}_n(\mathbb{C})$ and $\mathrm{PGL}_n(\mathbb{C})$ is a classical problem in the field of finite group theory, dating back to the late 19th century with authors like Klein, Jordan,…

We characterise when the C*-algebra C*(G) of a locally compact and Hausdorff groupoid G is subhomogeneous, that is, when its irreducible representations have bounded finite dimension; if so we establish a bound for its nuclear dimension in…

The genus gen(D) of a finite-dimensional central division algebra D over a field F is defined as the collection of classes [D'] in the Brauer group Br(F), where D' is a central division F-algebra having the same maximal subfields as D. For…

We show that the dimension of the Cuntz semigroup of a C*-algebra is determined by the dimensions of the Cuntz semigroups of its separable sub-C*-algebras. This allows us to remove separability assumptions from previous results on the…

The main purpose of this paper is to provide explicit computations of the fundamental group of several algebras. For this purpose, given a $k$-algebra $A$, we consider the category of all connected gradings of $A$ by a group $G$ and we…

We are interested in a class of groups, quasi-Frobenius groups (with involutions), whose internal structure generalizes that of the classical groups GA1(C), PGL 2(C) and SO3(R) : a subgroup and its conjugates, of finite index in their…

Permutation products and their various "fat diagonal" subspaces are studied from the topological and geometric point of view. We describe in detail the stabilizer and orbit stratifications related to the permutation action, producing a…

Let $p$ be a prime integer, $k$ be a $p$-closed field of characteristic $\neq p$, $T$ be a torus defined over $k$, $F$ be a finite $p$-group, and $1\to T \to G \to F \to 1$ be an exact sequence of algebraic groups. Extending earlier work of…

The prime graph of a finite group $G$, which is denoted by ${\rm GK}(G)$, is a simple graph whose vertex set is comprised of the prime divisors of $|G|$ and two distinct prime divisors $p$ and $q$ are joined by an edge if and only if there…

We consider fine G-gradings on M_n(C) (i.e. gradings of the matrix algebra over the complex numbers where each component is 1 dimensional). Groups which provide such a grading are known to be solvable. We consider the T-ideal of G-graded…

Based on recent successes concerning permutation resolutions of representations by Balmer and Gallauer we define a new invariant of finite groups: the p-permutation dimension. We define this analogously to the global dimension of a ring by…

Let D be a central division algebra of degree n over a field K. One defines the genus gen(D) of D as the set of classes [D'] in the Brauer group Br(K) of K represented by central division algebras D' of degree n over K having the same…

For a finite group $G$, we introduce a generalization of norm relations in the group algebra $\mathbb Q[G]$. We give necessary and sufficient criteria for the existence of such relations and apply them to obtain relations between the…