Related papers: Essential Dimension of Central Simple Algebras whe…

The goal of this note is to reduce the existing upper bound for the essential dimension of central simple algebras of degree 8 and exponent 2 over fields of characteristic 2 from 10 to 9.

Let $p$ be a prime integer, $1\leq s\leq r$ integers, $F$ a field of characteristic $p$. Let $\cat{Dec}_{p^r}$ denote the class of the tensor product of $r$ $p$-symbols and $\cat{Alg}_{p^r,p^s}$ denote the class of central simple algebras…

We give upper bounds on the essential dimension of (quasi-)simple algebraic groups over an algebraically closed field that hold in all characteristics. The results depend on showing that certain representations are generically free. In…

Let $1\leq m \leq n$ be integers with $m|n$ and $\cat{Alg}_{n,m}$ the class of central simple algebras of degree $n$ and exponent dividing $m$. In this paper, we find new, improved upper bounds for the essential dimension and 2-dimension of…

In this survey we discuss the results on the finitistic dimension of various stratified algebras. We describe what is already known, present some recent estimates, and list some open problems.

We give a survey of recent results related to the problem of characterizing finite-dimensional division algebras by the set of isomorphism classes of their maximal subfields. We also discuss various generalizations of this problem and some…

Let $A$ be an Artin algebra. We investigate subalgebras of $A$ with certain conditions and obtain some classes of algebras whose finitistic dimensions are finite.

A criterion for determining exactly when an order of a maximal subfield of a central simple algebra over a number field can be embedded into an order of this algebra is given. Various previous results have been generalized and recovered by…

We study the essential dimension of a finite group G over a field K. A generalization of the central extension theorem of Buhler and Reichstein (Compositio Math. 106 (1997) 159-179, Theorem 5.3) is obtained. We also get lower bounds of…

Motivated by the recent progress towards classification of simple finite-dimensional Lie algebras over an algebraically closed field of characteristic $2$, we investigate such $15$-dimensional algebras.

In this article the $p$-essential dimension of generic symbols over fields of characteristic $p$ is studied. In particular, the $p$-essential dimension of the length $\ell$ generic $p$-symbol of degree $n+1$ is bounded below by $n+\ell$…

We address the problem of when two finite dimensional central division algebras over the same field are necessarily isomorphic given that they have the same maximal subfields.

In this paper, we study the essential dimension of classes of central simple algebras with involutions of index less or equal to 4. Using structural theorems for simple algebras with involutions, we obtain the essential dimension of…

We define and study the essential dimension of an algebraic stack. We compute the essential dimension of the stacks Mgn and MgnBar of smooth, or stable, n-pointed curves of genus g. We also prove a general lower bound for the essential…

The maximal subalgebras of the finite dimensional simple special Jordan superalgebras over an algebraically closed field of characteristic 0 are studied. This is a continuation of a previous paper by the same authors about maximal…

We study maximal subalgebras of an arbitrary finite dimensional algebra over a field, and obtain full classification/description results of such algebras. This is done by first obtaining a complete classification in the semisimple case, and…

In this paper, we describe restricted one-dimensional central extensions of all finite dimensional simple restricted Lie algebras defined over fields of characteristic $p\ge 5$.

The finitistic dimension conjecture asserts that any finite-dimensional algebra over a field should have finite finitistic dimension. Recently, this conjecture is reduced to studying finitistic dimensions for extensions of algebras. In this…

We compare some algebras appeared in the recent attempts to prove resolution of singularities in positive characteristic. We also construct an algebra which encodes the same information and it is equivalent, up to integral closure, to the…

This paper is a further contribution to the extensive study by a number of authors of the subalgebra lattice of a Lie algebra. It is shown that, in certain circumstances, including for all solvable algebras, for all Lie algebras over…