Related papers: A gluing construction for polynomial invariants

We initiate a study of the rings of invariants of modular representations of elementary abelian p-groups. With a few notable exceptions, the modular representation theory of an elementary abelian p-group is wild. However, for a given…

Let $\Gamma$ be a finite group acting on a Lie group $G$. We consider a class of group extensions $1 \to G \to \hat{G} \to \Gamma \to 1$ defined by this action and a $2$-cocycle of $\Gamma$ with values in the centre of $G$. We establish and…

Let R be a commutative ring and let n,m be two positive integers. The symmetric group on n letters acts diagonally on the ring of polynomials in nxm variables with coefficients in R. The subrings of invariants for this action is called the…

Let $V$ be a real finite dimensional representation of a compact Lie group $G$. It is well-known that the algebra $\mathbb R[V]^G$ of $G$-invariant polynomials on $V$ is finitely generated, say by $\sigma_1,...,\sigma_p$. Schwarz proved…

Given a finite group $G$ and a generating set $S \subseteq G$, the diameter $diam(G,S)$ is the least integer $n$ such that every element of $G$ is the product of at most $n$ elements of $S$. In this paper, for bounded $|S|$, we characterize…

We present a construction, which assigns two groupoids, $\Gugamma$ and $\Gmgamma$, to an inverse semigroup $\Gamma$. By definition, $\Gmgamma$ is a subgroupoid (even a reduction) of $\Gugamma$. The construction unifies known constructions…

We show that (as conjectured by Lin and Wang) when a Vassiliev invariant of type $m$ is evaluated on a knot projection having $n$ crossings, the result is bounded by a constant times $n^m$. Thus the well known analogy between Vassiliev…

We show how there is associated to each non-constant polynomial $F(x,y)$ a completely integrable system with polynomial invariants on $\Rd$ and on $\C{2d}$ for each $d\geq1$; in fact the invariants are not only in involution for one Poisson…

We study actions of countable discrete groups which are amenable in the sense that there exists a mean on X which is invariant under the action of G. Assuming that G is nonamenable, we obtain structural results for the stabilizer subgroups…

Let $K$ be an algebraically closed field with characteristic zero, and $\mathfrak{g}$ a Lie algebra. Let $Y(\mathfrak{g})$ be the subalgebra of the symmetric algebra $S(\mathfrak{g})=K[\mathfrak{g}^*]$ made of the polynomials which are…

Given a group action, known by its infinitesimal generators, we exhibit a complete set of syzygies on a generating set of differential invariants. For that we elaborate on the reinterpretation of Cartan's moving frame by Fels and Olver…

For a finite group $G$, (semi-)Mackey functors and (semi-)Tambara functors are regarded as $G$-bivariant analogs of (semi-)groups and (semi-)rings respectively. In fact if $G$ is trivial, they agree with the ordinary (semi-)groups and…

The group invariance of entanglement is obtained within a very general and simple setup of the latter, given by a recently introduced considerably extended concept of tensor products. This general approach to entanglement - unlike the usual…

Let $A$ be the ring of integers of global field $K$. Let $G \subseteq GL_2(A)$ be a finite group. Let $G$ act linearly on $R = A[X,Y]$ (fixing $A$). Let $R^G$ be the ring of invariants. In the equi-characteristic case we prove $R^G$ is…

We introduce invariants of Hurwitz equivalence classes with respect to arbitrary group $G$. The invariants are constructed from any right $G$-modules $M$ and any $G$-invariant bilinear function on $M$, and are of bilinear forms. For…

For $\mathfrak{g}$ a simple Lie algebra and $G$ its adjoint group, the Chevalley map and work of Coxeter gives a concrete description of the algebra of $G$-invariant polynomials on $\mathfrak{g}$ in terms of traces over various…

Let $\mathcal{G}^{(\lambda)}$ be a group scheme which deforms $\mathbb{G}_a$ to $\mathbb{G}_m$. We explicitly describe the Cartier dual of the $l$-th Frobenius type kernel $N_l$ of the group scheme $\mathcal{E}^{(\lambda,\mu;D)}$ which is…

We study the interplay of the Golomb topology and the algebraic structure in polynomial rings $K[X]$ over a field $K$. In particular, we focus on infinite fields $K$ of positive characteristic such that the set of irreducible polynomials of…

The aim of this work is to extend the study of super-coinvariant polynomials, to the case of the generalized symmetric group $G_{n,m}$, defined as the wreath product $C_m\wr\S_n$ of the symmetric group by the cyclic group. We define a…

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.