Related papers: Essential dimension of reductive groups via generi…
We give a simple formula for the essential dimension of a finite pseudo-reflection group at a prime p and determine the absolute essential dimension for most irreducible pseudo-reflection groups. We also study the "poor man's essential…
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…
In this paper, we compute the essential $p$-dimension of the split finite quasi-simple groups of classical Lie type at the defining prime, specifically the quasi-simple groups arising from the general linear and special linear groups, the…
We introduce a technique for proving lower bounds on the essential dimension of split reductive groups. As an application, we strengthen the best previously known lower bounds for various split simple algebraic groups, most notably for the…
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…
We discuss the notion of essential dimension of a finite group and explain its relation with birational algebraic geometry. We show how this leads to a (partial) classification of simple finite groups of essential dimension less than or…
We determine the essential dimension of an arbitrary semisimple group of type $B$ of the form \[G=\big(\operatorname{\mathbf{Spin}}(2n_{1}+1)\times\cdots \times \operatorname{\mathbf{Spin}}(2n_{m}+1)\big)/\boldsymbol{\mu}\] over a field of…
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…
For some numerical semigroup rings of small embedding dimension, namely those of embedding dimension 3, and symmetric or pseudosymmetric of embedding dimension 4, presentations has been determined in the literature. We extend these results…
We compute the essential dimension of finite groups of order $\leqslant 63$.
One of the important open problems in the theory of central simple algebras is to compute the essential dimension of $\operatorname{GL}_n/\mu_m$, i.e., the essential dimension of a generic division algebra of degree $n$ and exponent…
We give an upper bound for the essential dimension of a smooth unipotent algebraic group over an arbitrary field. We also show that over a field $k$ which is finitely generated over a perfect field, a smooth unipotent algebraic $k$-group is…
We obtain upper bounds on the composition length of a finite permutation group in terms of the degree and the number of orbits, and analogous bounds for primitive, quasiprimitive and semiprimitive groups. Similarly, we obtain upper bounds…
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 produce a short and elementary algorithm to compute an upper bound for the canonical dimension of a spit semisimple linear algebraic group. Using this algorithm we confirm previously known bounds by Karpenko and Devyatov as well as we…
We classify the irreducible representations of smooth, connected affine algebraic groups over a field, by tackling the case of pseudo-reductive groups. We reduce the problem of calculating the dimension for pseudo-split pseudo-reductive…
We prove a new upper bound on the essential p-dimension of the projective linear group PGLn.
Several relations and bounds for the dimension of principal ideals in group algebras are determined by analyzing minimal polynomials of regular representations. These results are used in the two last sections. First, in the context of…
We determine the finite groups whose real irreducible representations have different degrees.
Finite semisimple group algebras for which all the minimal ideals are easily computable dimension (ECD) are characterized and some lower bounds for the minimum Hamming distance of group codes in these algebras are offered. Examples…