Related papers: Generators, Relations and Symmetries in Pairs of 3…

We give a computer-free proof that $J_2$ is isomorphic to the progenitor $2^{\star 32}: (2^{1+4}:A_5)$ factored by two relations, one of length 3 and and one of length 6, in the symmetric generators.

The factorization number $F_2(G)$ of a finite group $G$ is the number of all possible factorizations of $G=HK$ as product of its subgroups $H$ and $K$, while the subgroup commutativity degree $\mathrm{sd}(G)$ of $G$ is the probability of…

We study homomorphisms from $\mathrm{Out}(F_3)$ to $\mathrm{Out}(F_5)$, and $\mathrm{GL}(m,K)$ for $m < 7$, where $K$ is a field of characteristic other than 2 or 3. We conclude that all $K$-linear representations of dimension at most 6 of…

We study from an algebraic point of view the question of extending an action of a group \(\Gamma\) on a commutative domain \(R\) to a formal pseudodifferential operator ring \(B=R(\!(x\,;\,d)\!)\) with coefficients in \(R\), as well as to…

We introduce lattice models with explicit N=2 supersymmetry. In these interacting models, the supersymmetry generators Q^+ and Q^- yield the Hamiltonian H={Q^+,Q^-} on any graph. The degrees of freedom can be described as either fermions…

All supersymmetric gauge theories based on simple groups which have an affine quantum moduli space, i.e. one generated by gauge invariants with no relations, W=0, and anomaly matching at the origin, are classified. It is shown that the only…

In 2005, Shen introduced a new invariant, $\mathcal G(N)$, of a diffuse von Neumann algebra $N$ with a fixed faithful trace, and he used this invariant to give a unified approach to showing that large classes of ${\mathrm{II}}_1$ factors…

Generators and defining relations for wreath products of groups are given. Under some condition (conormality of the generators) they are minimal. In particular, it is just the case for the Sylow subgroups of the symmetric groups.

We describe a few properties of the non semi-simple associative algebra H = M_3 + (M_{2|1}(Lambda2))_0, where Lambda2 is the Grassmann algebra with two generators. We show that H is not only a finite dimensional algebra but also a (non…

Denote by $SL_3(\mathbb R)$ the special linear group of degree 3 over the real numbers, $A$ the subgroup consisting of the diagonal matrices with positive entries. In this paper, we study the algebraic and analytic properties of the…

A finite subgroup of the conformal group SL(2,C) can be related to invariant polynomials on a hypersurface in C^3. The latter then carries a simple singularity, which resolves by a finite iteration of basic cycles of deprojections. The…

Let R be a ring, M a nonzero left R-module, X an infinite set, and E the endomorphism ring of the direct sum of copies of M indexed by X. Given two subrings S and S' of E, we will say that S is equivalent to S' if there exists a finite…

Let $G$ be 2-generated group. The generating graph $\Gamma(G)$ of $G$ is the graph whose vertices are the elements of $G$ and where two vertices $g$ and $h$ are adjacent if $G = \langle g, h \rangle.$ This definition can be extended to a…

In Grayson's combinatorial description of higher K-groups, the generators are bounded acyclic binary multi-complexes of arbitrary size. Generalising work by Kasprowski, Winges and the author, we show in this paper that multi-complexes of…

A subgroup $H$ of a free group $F$ is called inert in $F$ if for every $G < F$ the rank of the intersection of $H$ with $G$ is no grater than the rank of $G$. In this paper we expand the known families of inert subgroups. We show that the…

For fields with more than $2$ elements, the classification of the vector spaces of matrices with rank at most $2$ is already known. In this work, we complete that classification for the field $\mathbb{F}_2$. We apply the results to obtain…

The generators and commutation relations are calculated explicitly for higher symmetry algebras of a class of hyperbolic Euler-Lagrange systems of Liouville type (in particular, for 2D Toda chains associated with semi-simple complex Lie…

Given a finite group scheme $\cG$ over an algebraically closed field $k$ of characteristic $\Char(k)=p>0$, we introduce new invariants for a $\cG$-module $M$ by associating certain morphisms $\deg^j_M : U_M \lra \Gr_d(M) \ \…

Let $G\subset SO(4)$ denote a finite subgroup containing the Heisenberg group. In these notes we classify all these groups, we find the dimension of the spaces of $G$-invariant polynomials and we give equations for the generators whenever…

We describe the relation between G-character varieties, $X_G(\Gamma)$, and $G/H$-character varieties, where $H$ is a finite, central subgroup of $G.$ In particular, we find finite generating sets of coordinate rings $C[X_{G/H}(\Gamma)]$ for…