Related papers: Kauffman Monoids

Let $(W,S)$ be an affine Coxeter system of type $\widetilde{B}$ or $\widetilde{D}$ and ${\rm TL}(W)$ the corresponding generalized Temperley-Lieb algebra. In this paper we define an infinite dimensional associative algebra made of decorated…

We study a monoid associated to complex semisimple Lie algebras, called the quantic monoid. Its monoid ring is shown to be isomorphic to a degenerate quantized enveloping algebra. Moreover, we provide normal forms and a straightening…

Given a finitely generated free monoid $X$ and a morphism $\phi : X\to X$, we show that one can construct an algebra, which we call an iterative algebra, in a natural way. We show that many ring theoretic properties of iterative algebras…

We prove the Freiheitssatz for right-symmetric algebras and the decidability of the word problem for right-symmetric algebras with a single defining relation. We also prove that two generated subalgebras of free right-symmetric algebras are…

Let G be a finite group that acts on an abelian monoid A. If f: A -> G is a map so that f(a f(a)(b)) = f(a)f(b), for all a, b in A, then the submonoid S = {(a, f(a)) | a in A} of the associated semidirect product of A and G is said to be a…

For a diagram automorphism of an affine Kac-Moody algebra such that the folded diagram is still an affine Dynkin diagram, we show that the associated Drinfeld-Sokolov hierarchy also admits an induced automorphism. Then we show how to obtain…

We first show that the moniod of separable surjective self morphisms of a variety of Ueno type coincides with the group of automorphisms. We also give an explicit description of the automorphism group. As applications, we confirm Kawaguchi…

We prove that the group of automorphisms of the Lie algebra $\Der_K (P_n)$ of derivations of a polynomial algebra $P_n=K[x_1,..., x_n]$ over a field of characteristic zero is canonically isomorphic to the the group of automorphisms of the…

The monoidal category of Soergel bimodules categorifies the Hecke algebra of a finite Weyl group. In the case of the symmetric group, morphisms in this category can be drawn as graphs in the plane. We define a quotient category, also given…

Let $\mathrm{HK}_{\Theta}$ denote the Hecke-Kiselman monoid associated to a finite simple oriented graph $\Theta$. We present a Boolean matrix monoid that is isomorphic to the endomorphism monoid $\mathrm{End}(\mathrm{HK}_{\Theta})$.

We show that the derived center of the category of simplicial algebras over every algebraic theory is homotopically discrete, with the abelian monoid of components isomorphic to the center of the category of discrete algebras. For example,…

We describe, up to degree equal to the rank, the Lie algebra associated with the automorphism group of a free group. We compute in particular the ranks of its homogeneous components, and their structure as modules over the linear group.…

Bergman has given the following abstract characterisation of the inner automorphisms of a group $G$: they are exactly those automorphisms of $G$ which can be extended functorially along any homomorphism $G \rightarrow H$ to an automorphism…

The polynomial automorphisms of the affine plane over a field K form a group which has the structure of an amalgamated free product. This well-known algebraic structure can be used to determine some key results about the symmetry and…

We study integrals of Hopf monoids in duoidal endohom categories of naturally Frobenius map monoidales in monoidal bicategories. We prove two Maschke type theorems, relating the separability of the underlying monoid and comonoid,…

In this paper we study regular irreducible algebraic monoids over $\fldc$ equipped with the euclidean topology. It is shown that, in such monoids, the Green classes and the spaces of idempotents in the Green classes all have natural…

The Temperley-Lieb algebra is a fundamental component of SU(2) topological quantum field theories. We construct chain complexes corresponding to minimal idempotents in the Temperley-Lieb algebra. Our results apply to the framework which…

The Toroidal Lie algebras are n variable genaralizations of Affine Kac-Moody Lie algebras. As in the affine Lie algebras there exists finite order auto= morphisms corresponding to Dynkin diagram automorphisms. The fixed point sub= algebras…

We present simple graph-theoretic characterizations of Cayley graphs for monoids, semigroups and groups. We extend these characterizations to commutative monoids, semilattices, and abelian groups.

We introduce two new algebras that we call \emph{tied--boxed Hecke algebra} and \emph{tied--boxed Temperley--Lieb algebra}. The first one is a subalgebra of the algebra of braids and ties introduced by Aicardi and Juyumaya, and the second…