Related papers: Computing invariants of algebraic group actions in…

In this expository note we discuss a class of graded algebras named Cox rings, which are naturally associated to algebraic varieties generalizing the homogeneous coordinate rings of projective spaces. Whenever the Cox ring is finitely…

We study conditions under which subdirect products of various types of algebraic structures are finitely generated or finitely presented. In the case of two factors, we prove general results for arbitrary congruence permutable varieties,…

Let $k$ be a field, let $G$ be a reductive algebraic group over $k$, and let $V$ be a linear representation of $G$. Geometric invariant theory involves the study of the $k$-algebra of $G$-invariant polynomials on $V$, and the relation…

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 explore connected affine algebraic groups $G$, which enjoy the following finiteness property $\rm (F)$: for every algebraic action of $G$, the closure of every $G$-orbit contains only finitely many $G$-orbits. We obtain two main results.…

We generalize the theory of the second invariant cohomology group $H^2_{\rm inv}(G)$ for finite groups $G$, developed in [Da2,Da3,GK], to the case of affine algebraic groups $G$, using the methods of [EG1,EG2,G]. In particular, we show that…

A very classical subject in Commutative Algebra is the Invariant Theory of finite groups. In our work on 3-dimensional topology (S. King, Ideal Turaev-Viro invariants. To appear in Top. Appl.), we found certain examples of group actions on…

We find finite, reasonably small, generator sets of the coordinate rings of G-character varieties of finitely generated groups for all classical groups G. This result together with the method of Grobner basis gives an algorithm for…

If G is a finitely generated group, and A an algebraic group, then Hom(G,A) is a possibly reducible algebraic variety denoted by R_A(G). Here we define the profile function, P_d(R_A(G)), of the representation variety of G over A to be…

We study degree bounds on rational but not necessarily polynomial generators for the field $\mathbf{k}(V)^G$ of rational invariants of a linear action of a finite abelian group. We show that lattice-theoretic methods used recently by the…

For a locally compact group G and a compact subgroup K, the corresponding Hecke algebra consists of all continuous compactly supported complex functions on G that are K-bi-invariant. There are many examples of totally disconnected locally…

Let $G$ be a complex classical group, and let $V$ be its defining representation (possibly plus a copy of the dual). A foundational problem in classical invariant theory is to write down generators and relations for the ring of…

A characterization of finitely generated shift-invariant subspaces is given when generators are g-minimal. An algorithm is given for the determination of the coefficients in the well known representation of the Fourier transform of an…

The problem of characterizing GKLS-generators and CP-maps with an invariant appeared in different guises in the literature. We prove two unifying results which hold even for weakly closed *-algebras: First, we show how to construct a normal…

Computation of polynomial relative invariants is a classical tool in algebra. Relative differential invariants are central for the equivalence problem of geometric structures. We address the fundamental problem of finite generation of their…

If $G$ is an algebraic affine group acting on an affine variety $X$, there is a natural notion of covariant representation for the pair $(G,X)$. In this paper, we classify the irreducible covariant representations for any such pair by…

For G=SL_n or GL_n we construct representations V such that the invariant ring K[V]^G is not Cohen-Macaulay.

Let (G,G^+) be a simple ordered abelian group. We say that G has strong perforation if there exists a non-positive element x in G such that nx is positive and non-zero for some natural number n. Otherwise, the group is said to be weakly…

If $G$ is a countable, discrete group generated by two finite subgroups $H$ and $K$ and $P$ is a II$_1$ factor with an outer G-action, one can construct the group-type subfactor $P^H \subset P \rtimes K$ introduced in \cite{BH}. This…

Suppose that G is a linearly reductive group. We study the minimal free resolution of the invariant ring. If G is a finite linearly reductive group, then the ring of invariants is generated in degree at most |G|, the group order. We prove…