Related papers: Invariants of finite group schemes

Using the geometric quotient of a real algebraic set by the action of a finite group G, we construct invariants of GAS sets with respect to equivariant homeomorphisms with AS-graph, including additive invariants with values in Z.

We show that if a flat group scheme acts properly, with finite stabilizers, on an algebraic space, then a quotient exists as a separated algebraic space. More generally we show any flat groupid for which the family of stabilizers is finite…

This paper extends classical results in the invariant theory of finite groups and finite group schemes to the actions of finite Hopf algebras on commutative rings.

We study algebraicity and smoothness of fixed point stacks for flat group schemes which have a finite composition series whose factors are either reductive or proper, flat, finitely presented, acting on algebraic stacks with affine,…

Let $K$ be a field and $f:\mathbb{P}^N \to \mathbb{P}^N$ a morphism. There is a natural conjugation action on the space of such morphisms by elements of the projective linear group $\text{PGL}_{N+1}$. The group of automorphisms, or…

We investigate compact quantum group actions on unital $C^*$-algebras by analyzing invariant subsets and invariant states. In particular, we come up with the concept of compact quantum group orbits and use it to show that countable compact…

We explore orbits, rational invariant functions, and quotients of the natural actions of connected, not necessarily finite dimensional subgroups of the automorphism groups of irreducible algebraic varieties. The applications of the results…

The first part of this paper is a refinement of Winkelmann's work on invariant rings and quotients of algebraic groups actions on affine varieties, where we take a more geometric point of view. We show that the (algebraic) quotient…

Let $G$ be an affine algebraic group over an algebraically closed field $k$ of characteristic zero. In this paper, we consider finite $G$-equivariant morphisms $F:X\to Y$ of irreducible affine $G$-varieties. First we determine under which…

We exhibit invariants of smooth projective algebraic varieties with integer values, whose nonvanishing modulo p prevents the existence of an action without fixed points of certain finite p-groups. The case of base fields of characteristic p…

Geometric Invariant Theory gives a method for constructing quotients for group actions on algebraic varieties which in many cases appear as moduli spaces parametrizing isomorphism classes of geometric objects (vector bundles, polarized…

Let $k$ be a field, let $G$ be a reductive group, and let $V$ be a linear representation of $G$. Let $V//G = Spec(Sym(V^*))^G$ denote the geometric quotient and let $\pi: V \to V//G$ denote the quotient map. Arithmetic invariant theory…

This is a survey on the automorphism groups in various classes of affine algebraic surfaces and the algebraic group actions on such surfaces. Being infinite-dimensional, these automorphism groups share some important features of algebraic…

We consider a class of homogeneous manifolds over a simple Lie group which appears in the problem of classification of homogeneous manifolds with reductive subgroups of maximal rank as stabilizer of a point. We prove that any manifold of…

Some consequences of a $qp$-quantization of a point group invariant developed in the enveloping algebra of $SU(2)$ are examined in the present note. A set of open problems concerning such invariants in the $U_{qp}(u(2))$ quantum algebra…

We use Sigma-invariants to study homotopical and homological finiteness properties of fixed subgroups of automorphisms of a group $G$ in terms of its center $Z(G)$ and the induced automorphisms on its associated quotient $G/Z(G)$.…

We prove finite generation of the algebras of invariants for a class of linear actions of suitable non-reductive groups on projective and affine varieties, and give a geometric construction for their GIT quotients.

We study the invariant theory of a class of quantum Weyl algebras under group actions and prove that the fixed subrings are always Gorenstein. We also verify the Tits alternative for the automorphism groups of these quantum Weyl algebras.

We survey recent results on multiple transitivity of automorphism groups of affine algebraic varieties. We consider the property of infinite transitivity of the special automorphism group, which is equivalent to flexibility of the…

In this paper we describe a family of isomorphism invariants of a finitely generated Coxeter group W. Each of these invariants is the isomorphism type of a quotient group W/N of W by a characteristic subgroup N. The virtue of these…