Related papers: Generating groups using hypergraphs

We consider the ring of coinvariants for modular representations of cyclic groups of prime order. For all cases for which explicit generators for the ring of invariants are known, we give a reduced Gr\"obner basis for the Hilbert ideal and…

We extend the methods of geometric invariant theory to actions of non--reductive groups in the case of homomorphisms between decomposable sheaves whose automorphism groups are non--reductive. Given a linearization of the natural action of…

Based on work done by Bonechi, Cattaneo, Felder and Zabzine on Poisson sigma models, we formally show that Kontsevich's star product can be obtained from the twisted convolution algebra of the geometric quantization of a Lie 2-groupoid, one…

In this article we study the structure of $\Gamma$-invariant spaces of $L^2(\bf R)$. Here $\bf R$ is a second countable LCA group. The invariance is with respect to the action of $\Gamma$, a non commutative group in the form of a semidirect…

Equivariant Loday constructions are a means for providing geometric interpretations of equivariant homology theories. They are usually constructed for a simplicial $G$-set and a $G$-Tambara functor. We study situations where -- depending on…

Let G be an algebraic group and let X be a generically free G-variety. We show that X can be transformed, by a sequence of blowups with smooth G-equivariant centers, into a G-variety X' with the following property: the stabilizer of every…

In order to enumerate the fake projective planes, as announced in~\cite{CS}, we found explicit generators and a presentation for each maximal arithmetic subgroup $\bar\Gamma$ of~$PU(2,1)$ for which the (appropriately normalized) covolume…

Harding showed that the direct product decompositions of many different types of structures, such as sets, groups, vector spaces, topological spaces, and relational structures, naturally form orthomodular posets. When applied to the direct…

We explicitly construct generators of the rational homotopy groups of the space of stable h-cobordisms of the classifying space of a cyclic group of order n by generalizing a construction of Hatcher. This result will be used in a separate…

The main objective of the present work is to study contraction semigroups generated by Laplace operators on metric graphs, which are not necessarily self-adjoint. We prove criteria for such semigroups to be continuity and positivity…

Given an algebra $F[H]^G$ of polynomial invariants of an action of the group $G$ over the vector space $H$, a subset $S$ of $F[H]^G$ is called separating if $S$ separates all orbits that can be separated by $F[H]^G$. A minimal separating…

We show that special cycles generate a large part of the cohomology of locally symmetric spaces associated to orthogonal groups. We prove in particular that classes of totally geodesic submanifolds generate the cohomology groups of degree…

Hyperelliptic mapping class groups are defined either as the centralizers of hyperelliptic involutions inside mapping class groups of oriented surfaces of finite type or as the inverse images of these centralizers by the natural…

The problem of finding generators of the subalgebra of invariants under the action of a group of automorphisms of a finite dimensional Lie algebra on its universal enveloping algebra is reduced to finding homogeneous generators of the same…

To each projective hypersurface which is not a cone, we associate an abelian linear algebraic group called the symmetrizer group of the corresponding symmetric form. This group describes the set of homogeneous polynomials with the same…

We show that in a stable first-order theory, the failure of higher-dimensional type amalgamation can always be witnessed by algebraic structures which we call n-ary polygroupoids. This generalizes a result of Hrushovski that failures of…

We study algebras of meromorphic modular forms whose poles lie on Heegner divisors for orthogonal and unitary groups associated to root lattices. We give a uniform construction of $147$ hyperplane arrangements on type IV symmetric domains…

The results of computer computations determining the automorphism groups of the groups of order 32$p$ for $p \geq 3$ are given in several tables. Presentations for the automorphism groups of the groups of order 32, which in many cases…

We construct a family of groups from suitable higher rank graphs which are analogues of the finite symmetric groups. We introduce homological invariants showing that many of our groups are, for example, not isomorphic to $nV$, when $n \geq…

We study connected components of the Morse boundary and their stabilisers. We introduce the notion of point-convergence and show that if the set of non-singleton connected components of the Morse boundary of a finitely generated group $G$…