Related papers: Presentations of matrix rings
Matrices over the ring of formal power series are considered. Normal forms with respect to various sub-groups of the two-sided transformations are constructed. The construction is based on the special property of the action: it induces a…
We introduce a presentation of the Chow ring of a matroid by a new set of generators, called "simplicial generators." These generators are analogous to nef divisors on projective toric varieties, and admit a combinatorial interpretation via…
We give a monoid presentation in terms of generators and defining relations for the partial analogue of the finite dual inverse symmetric monoid.
This paper gives a new, simplified presentation of the classical pure braid group. The generators are given by the squares of the longest elements over connected subgraphs, and we prove that the only relations are either commutators or…
Direct powers of perfect groups admit more concise presentations than one might naively suppose. If $H_1G=H_2G=0$, then $G^n$ has a presentation with $O(\log n)$ generators and $O(\log n)^3$ relators. If, in addition, there is an element…
We investigate the representation theory of some recently constructed N=2 super W-algebras with two generators. Except for the central charges in the unitary minimal series of the N=2 super Virasoro algebra we find no new rational models.…
Gruenberg and Linnell showed that the standard relation module of a free product of $n$ groups of the form $C_r \times \mathbb{Z}$ could be generated by just $n+1$ generators, raising the possibility of a relation gap. We explicitly give…
In this paper we study the minimal number of generators for simple Lie algebras in characteristic 0 or p > 3. We show that any such algebra can be generated by 2 elements. We also examine the 'one and a half generation' property, i.e. when…
A construction that generates Williamson matrices of order $2n$ from Williamson matrices of odd order $n$ is presented. The construction is completely constructive and only uses three simple sequence operations.
Let $L$ be a link in $S^3$. We consider the class of meridional presentations for $\pi_1(S^3\backslash L)$ in which the relations are witnessed by embedded two-spheres which can be represented simultaneously in a fixed diagram of $L$,…
We show that all spin groups of non-definite, quinary quadratic forms over a field with characteristic 0 can be represented as 2 by 2 matrices with entries in an associated quaternion algebra. Over local and global fields, we further study…
The iteration of rational maps is well-understood in dimension 1 but less so in higher dimensions. We study some maps on spaces of matrices which present a weak complexity with respect to the ring structure. First we give some properties of…
The orthogonal group acts on the space of several $n\times n$ matrices by simultaneous conjugation. For an infinite field of characteristic different from two, relations between generators for the algebra of invariants are described. As an…
We study low-dimensional representations of matrix groups over general rings, by considering group actions on CAT(0) spaces, spheres and acyclic manifolds.
For certain rings $\mathcal{R}$, we construct explicit matrices representing nonzero classes in the algebraic $K$ theory group $NK_{1}(\mathcal{R})$.
A nilpotent quotient algorithm for finitely presented Lie rings over Z (LieNQ) is described. The paper studies graded and non-graded cases separately. The algorithm computes the so-called nilpotent presentation for a finitely presented,…
Over a field of characteristic 0, the algebra of invariants of several $n\times n$ matrices under simultaneous conjugation by $GL_n$ is generated by traces of products of generic matrices. In this paper we have found, in terms of…
This note gives generators and relations for the strict monoidal category of probabilistic maps on finite cardinals (i.e., stochastic matrices).
In this paper we give a technique to represent simple connected graphs by using Clockwise Circular Representations and we show its applications by calculating orthogonal representations of simple connected graphs which are essentials in…
We give a simple and explicit presentation of the Z/2-equivariant complex cobordism ring.