Related papers: On presentations of Brauer-type monoids

This is the first in a series of papers in which we study representations of the Brauer category and its allies. We define a general notion of triangular category that abstracts key properties of the triangular decomposition of a semisimple…

This paper investigates the homology of the Brauer algebras, interpreted as appropriate Tor-groups, and shows that it is closely related to the homology of the symmetric group. Our main results show that when the defining parameter of the…

Ramified monoids are a class of monoids introduced by the authors. The main motivation for considering these monoids comes from knot theory, see [3, 4, 5]. Thus, in [2] we have studied the ramified monoids of the symmeytric group and of the…

We describe the structure of finite Boolean inverse monoids and apply our results to the representation theory of finite inverse semigroups. We then generalize to semisimple Boolean inverse semigroups.

We study arithmetic properties of factorizations of elements into products of generators, in monoids given with explicit presentations. After relating and comparing this perspective to the more usual approach of factoring into products of…

Starting from the geometric construction of the framed braid group, we define and study the framization of several Brauer-type monoids and also the set partition monoid, all of which appear in knot theory. We introduce the concept of…

In the paper we give a survey of rather new notions and results which generalize classical ones in the theory of braids. Among such notions are various inverse monoids of partial braids. We also observe presentations different from standard…

We construct certain monoids, called tied monoids. These monoids result to be semidirect products finitely presented and commonly built from braid groups and their relatives acting on monoids of set partitions. The nature of our monoids…

A variant of a semigroup $S$ with respect to an element $a\in S$ is the semigroup $S^{a}=(S,\star_{a})$, where $x\star_{a}y=xay$ for any $x,y\in S$. Here, $a$ is the sandwich element of $S^{a}$. In this article, we study variants of the…

In this paper, we consider the monoids of all partial endomorphisms, of all partial weak endomorphisms, of all injective partial endomorphisms, of all partial strong endomorphisms and of all partial strong weak endomorphisms of a star graph…

We show that all Sugihara monoids can be represented as algebras of binary relations, with the monoid operation given by relational composition. Moreover, the binary relations are weakening relations. The first step is to obtain an explicit…

We give presentations, in terms of generators and relations, for the monoids of singular braids on closed surfaces. The proof of the validity of these presentations can also be applied to verify, in a new way, the presentations given by…

We give a complete description of the congruences on the partition monoid $P_X$ and the partial Brauer monoid $PB_X$, where $X$ is an arbitrary infinite set, and also of the lattices formed by all such congruences. Our results complement…

We describe and count the maximal subsemigroups of many well-known monoids of transformations and monoids of partitions. More precisely, we find the maximal subsemigroups of the full spectrum of monoids of order- or orientation-preserving…

We introduce and study several affine (=annular in this paper) versions of the classical diagram algebras such as Temperley-Lieb, partition, Brauer, Motzkin, rook Brauer, rook, planar partition, and planar rook algebras. We give generators…

In this short note we observe that the recent examples of derived-equivalent Calabi-Yau 3-folds with different fundamental groups also have different Brauer groups, using a little topological K-theory.

The Brauer category is a symmetric strict monoidal category that arises as a categorification of the Brauer algebras in the context of Banagl's framework of positive topological field theories (TFTs). We introduce the chromatic Brauer…

Classical diagram categories and monoids, including the Temperley--Lieb, Brauer, and partition cases, arise as special instances of the category of two dimensional cobordisms and admit additional twists that produce a large new family of…

By the theorems of Cayley and Vagner-Preston, the full transformation monoids and the symmetric inverse monoids play analogous roles in the theory of monoids and inverse monoids, as the symmetric groups do in the theory of groups. Every…

A category of Brauer diagrams, analogous to Turaev's tangle category, is introduced, and a presentation of the category is given; specifically, we prove that seven relations among its four generating homomorphisms suffice to deduce all…