Related papers: Finite Groups of Essential Dimension 2
We prove that if a finite group scheme $G$ over a field $k$ has essential dimension one, then it embeds in $PGL_{2/k}$. We use this to give an explicit classification of all infinitesimal group schemes of essential dimension one over any…
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…
Let K be an arbitrary field. We will determine explicitly all the nontrivial finite groups of essential dimension one over K.
Given a finite smooth group scheme $G$ over a field of characteristic $p > 0$, we show that the essential dimension of $G$ at $p$ is $0$ when $p$ does not divide the order of $G$, and $1$ when it does.
We classify quasi-simple finite groups of essential dimension 3.
We compute the essential dimension of finite groups of order $\leqslant 63$.
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…
Using the algebraic classification of all $2$-dimensional algebras, we give the algebraic classification of all $2$-dimensional rigid, conservative and terminal algebras over an algebraically closed field of characteristic 0. We have the…
We develop new techniques to classify basic algebras of blocks of finite groups over algebraically closed fields of prime characteristic. We apply these techniques to simplify and extend previous classifications by Linckelmann, Murphy and…
We determine the essential dimension of the spin group Spin(n) as an algebraic group over a field of characteristic 2, for n at least 15. In this range, the essential dimension is the same as in characteristic not 2. In particular, it is…
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…
In this paper we describe all group gradings by a finite abelian group $\Gamma$ of a simple Lie algebra of type $G_2$ over an algebraically closed field $F$ of characteristic 0.
We shall define a general notion of dimension, and study groups and rings whose interpretable sets carry such a dimensio. In particular, we deduce chain conditions for groups, definability results for fields and domains, and show that…
In this paper we find a characterization for groups elementarily equivalent to a free nilpotent group $G$ of class 2 and arbitrary finite rank.
This work completes the classification of the imprimitive irreducible modules, over algebraically closed fields of characteristic 0, of the finite quasisimple groups.
We determine the finite groups whose real irreducible representations have different degrees.
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…
We classify, up to isomorphism, all gradings by an arbitrary abelian group on simple finitary Lie algebras of linear transformations (special linear, orthogonal and symplectic) on infinite-dimensional vector spaces over an algebraically…
A complete classification of two-dimensional algebras over algebraically closed fields is provided
We classify, up to conjugacy, the finite (constant) subgroups G of adjoint absolutely simple algebraic groups of type $A_1$ over an arbitrary field $k$ of characteristic not 2.