Related papers: Autometrized Lattice Ordered Monoids
Loday's assembly maps approximate the K-theory of group rings by the K-theory of the coefficient ring and the corresponding homology of the group. We present a generalization that places both ingredients on the same footing. Building on…
A modular or distributive lattice is `diamond-colored' if its order diagram edges are colored in such a way that, within any diamond of edges, parallel edges have the same color. Such lattices arise naturally in combinatorial representation…
We characterize the fixed sets of automorphisms of an arbitrary countable, arithmetically saturated structure.
We characterize numerical semigroups for which the poset of its ideal class monoid is a lattice, and study the irreducible elements of such a lattice with respect to union, intersection, infimum and supremum.
We provide a generalization of Mundici's equivalence between unital Abelian lattice-ordered groups and MV-algebras: the category of unital commutative lattice-ordered groups is equivalent to the category of MV-monoidal algebras. Roughly…
R. Canfield has conjectured that for all subgroups G of the automorphism group of the Boolean lattice B(n) (which can be regarded as the symmetric group S(n)) the quotient order B(n)/G is a symmetric chain order. We provide a…
In this paper we present a definition of oriented Lagrangian symplectic matroids and their representations. Classical concepts of orientation and this extension may both be thought of as stratifications of thin Schubert cells into unions of…
We introduce the notion of left (and right) quasi-Loday algebroids and a "universal space" for them, called a left (right) omni-Loday algebroid, in such a way that Lie algebroids, omni-Lie algebras and omni-Loday algebroids are particular…
We characterize the equational theories and Lawvere theories that correspond to the categories of analytic and polynomial monads on Set, and hence also the categories of the symmetric and rigid operads in Set. We show that the category of…
The paper presents the complete classification of Automorphic Lie Algebras based on $\mathfrak{sl}_n (\mathbb{C})$, where the symmetry group $G$ is finite and the orbit is any of the exceptional $G$-orbits in $\overline{\mathbb{C}}$. A key…
We are concerned with orderable groups and particularly those with orderings invariant not only under multiplication, but also under a given automorphism or family of automorphisms. Several applications to topology are given: we prove that…
The aim of this paper is to establish a lattice theoretical framework to study the partially ordered set $\operatorname{\mathsf{tors}} A$ of torsion classes over a finite-dimensional algebra $A$. We show that $\operatorname{\mathsf{tors}}…
This paper deals with graph automaton groups associated with trees and some generalizations. We start by showing some algebraic properties of tree automaton groups. Then we characterize the associated semigroup, proving that it is…
We compute the monoid $V(L_K(E))$ of isomorphism classes of finitely generated projective modules over certain graph algebras $L_K(E)$, and we show that this monoid satisfies the refinement property and separative cancellation. We also show…
In this paper, we introduce a notion of a left-symmetric algebroid, which is a generalization of a left-symmetric algebra from a vector space to a vector bundle. The left multiplication gives rise to a representation of the corresponding…
As algebraic semantics of the logic of quantum mechanics there are usually used orthomodular posets, i.e. bounded posets with a complementation which is an antitone involution and where the join of orthogonal elements exists and the…
Arithmetical invariants---such as sets of lengths, catenary and tame degrees---describe the non-uniqueness of factorizations in atomic monoids. We study these arithmetical invariants by the monoid of relations and by presentations of the…
Matroids and semigraphoids are discrete structures abstracting and generalizing linear independence among vectors and conditional independence among random variables, respectively. Despite the different nature of conditional independence…
We investigate the monoid of transformations that are induced by sequences of writing to and reading from a queue storage. We describe this monoid by means of a confluent and terminating semi-Thue system and study some of its basic…
Every transformation monoid comes equipped with a canonical topology-the topology of pointwise convergence. For some structures, the topology of the endomorphism monoid can be reconstructed from its underlying abstract monoid. This…