Related papers: Algebraic fundamental group and simplicial complex…

In this article it is determined which integral reflection representations of the symmetric groups and the primitive complex reflection groups of degree $2$ have rings of invariants which are isomorphic to polynomial rings.

We show that a fundamental sandwich algebra has an analogue of a root system of a semisimple Lie algebra. This leads to an analogue of a Weyl group, which we study in another paper.

We obtain a complete classification of minimal simple unitary $W$-algebras.

We derive presentation and relations for a group of compact Riemann surface that is given as branched cover of the sphere. In the case that one of the permutations is of full cycle of the form $(1...n)$ we derive a straightforward process…

In answer to a question of P. Hall, we supply another construction of a group which is isomorphic to each of its non-trivial normal subgroups.

We show how one can do algebraic geometry with respect to the category of simplicial objects in an exact category. As a biproduct, we get a theory of derived analytic geometry.

We prove that an irreducible lattice in a semisimple algebraic group is virtually isomorphic to an arithmetic lattice if and only if it admits a faithful self-similar action on a rooted tree of finite valency.

We generalize the theory of critical groups from graphs to simplicial complexes. Specifically, given a simplicial complex, we define a family of abelian groups in terms of combinatorial Laplacian operators, generalizing the construction of…

An algorithm for the explicit computation of a complete set of primitive central idempotents, Wedderburn decomposition and the automorphism group of the semisimple group algebra of a finite metabelian group is developed. The algorithm is…

We establish an upper bound on the cardinality of a minimal generating set for the fundamental group of a large family of connected, balanced simplicial complexes and, more generally, simplicial posets.

This paper studies simplicity, primitivity and semiprimitivity of algebras associated to \'etale groupoids. Applications to inverse semigroup algebras are presented. The results also recover the semiprimitivity of Leavitt path algebras and…

We show that the classification of simple finite group schemes over an algebraically closed field reduces to the classification of abstract simple finite groups and of simple restricted Lie algebras in positive characteristic. Both these…

Let $A$ be an $n$-dimensional algebra over a field $k$ and $a(A)$ its quantum symmetry semigroup. We prove that the automorphisms group ${\rm Aut}_{\rm Alg} (A)$ of $A$ is isomorphic to the group $U \bigl( G(a (A)^{\rm o} ) \bigl)$ of all…

Isomorphy classes of k-involutions have been studied for their correspondence with generalized symmetric spaces of algebraic groups. This is a continuation of papers written by A.G. Helminck and collaborators that are regarding algebraic…

In this paper we study the classifying spaces of graph products of simplicial groups and connected Hopf algebras over a field, and show that they can be uniformly treated under the framework of polyhedral products. It turns out that these…

For finite nilpotent groups $G$ and $G^{\prime}$, and a $G$-adapted ring $S$ (the rational integers, for example), it is shown that any isomorphism between the centers of the group rings $SG$ and $SG^{\prime}$ is monomial, i.e., maps class…

We complete the description of group gradings on finite-dimensional incidence algebras. Moreover, we classify the finite-dimensional graded algebras that can be realized as incidence algebras endowed with a group grading.

For every finite abelian group $G$, there are positive integers $n$ and $d$ such that $G$ is isomorphic to the multiplicative group of $d$-th powers of reduced residues modulo $n$.

In previous work, we showed that there are appropriate model category structures on the category of simplicial categories and on the category of Segal precategories, and that they are Quillen equivalent to one another and to Rezk's complete…

Generalizing homogeneous spectra for rings graded by natural numbers, we introduce multihomogeneous spectra for rings graded by abelian groups. Such homogeneous spectra have the same completeness properties as their classical counterparts,…