Results 21 to 30 of about 2,424 (82)

Quivers of monoids with basic algebras

, 2011
We compute the quiver of any monoid that has a basic algebra over an algebraically closed field of characteristic zero. More generally, we reduce the computation of the quiver over a splitting field of a class of monoids that we term rectangular monoids (
Aguiar, Almeida, Auslander, Benjamin Steinberg, Benson, Borceux, Brown, Brown, Cartan, Cline, Curtis, Denton, Denton, Eilenberg, Ganyushkin, Hsiao, James, Johnstone, Koucký, Krohn, Mac Lane, Mac Lane, Putcha, Renner, Steinberg, Stuart Margolis, Tits, Webb   +27 more
core   +1 more source

A coboundary Temperley–Lieb category for sl2$\mathfrak {sl}_{2}$‐crystals

Journal of the London Mathematical Society, Volume 112, Issue 3, September 2025.
Abstract By considering a suitable renormalization of the Temperley–Lieb category, we study its specialization to the case q=0$q=0$. Unlike the q≠0$q\ne 0$ case, the obtained monoidal category, TL0(k)$\mathcal {TL}_0(\mathbb {k})$, is not rigid or braided. We provide a closed formula for the Jones–Wenzl projectors in TL0(k)$\mathcal {TL}_0(\mathbb {k})$
Moaaz Alqady, Mateusz Stroiński
wiley   +1 more source

On Varieties of Automata Enriched with an Algebraic Structure (Extended Abstract)

, 2014
Eilenberg correspondence, based on the concept of syntactic monoids, relates varieties of regular languages with pseudovarieties of finite monoids.
Klíma, Ondřej
core   +2 more sources

On the dimension of orthogonal projections of self‐similar measures

Journal of the London Mathematical Society, Volume 112, Issue 1, July 2025.
Abstract Let ν$\nu$ be a self‐similar measure on Rd$\mathbb {R}^d$, d⩾2$d\geqslant 2$, and let π$\pi$ be an orthogonal projection onto a k$k$‐dimensional subspace. We formulate a criterion on the action of the group generated by the orthogonal parts of the iterated function system on π$\pi$, and show that it ensures that the dimension of πν$\pi \nu$ is
Amir Algom, Pablo Shmerkin
wiley   +1 more source

On the isomorphism problem for monoids of product‐one sequences

Bulletin of the London Mathematical Society, Volume 57, Issue 5, Page 1482-1495, May 2025.
Abstract Let G1$G_1$ and G2$G_2$ be torsion groups. We prove that the monoids of product‐one sequences over G1$G_1$ and over G2$G_2$ are isomorphic if and only if the groups G1$G_1$ and G2$G_2$ are isomorphic. This was known before for abelian groups.
Alfred Geroldinger, Jun Seok Oh
wiley   +1 more source

Ordered groupoids and the holomorph of an inverse semigroup

, 2014
We present a construction for the holomorph of an inverse semigroup, derived from the cartesian closed structure of the category of ordered groupoids.
CJ Isham, DB McAlister, DB McAlister, E. A. McDougall, J Certaine, JS Rose, M Kunze, M Nivat, MV Lawson, N. D. Gilbert, ND Gilbert, R Baer, R Brown, RJ Warne, WR Nico   +14 more
core   +1 more source

On minimal presentations of numerical monoids

Bulletin of the London Mathematical Society, Volume 57, Issue 3, Page 878-894, March 2025.
Abstract We consider the classical problem of determining the largest possible cardinality of a minimal presentation of a numerical monoid with given embedding dimension and multiplicity. Very few values of this cardinality are known. In addressing this problem, we apply tools from Hilbert functions and free resolutions of artinian standard graded ...
Alessio Moscariello, Alessio Sammartano
wiley   +1 more source

Markov chains, $\mathscr R$-trivial monoids and representation theory

, 2014
We develop a general theory of Markov chains realizable as random walks on $\mathscr R$-trivial monoids. It provides explicit and simple formulas for the eigenvalues of the transition matrix, for multiplicities of the eigenvalues via M\"obius inversion ...
Ayyer, Arvind, Schilling, Anne, Steinberg, Benjamin, Thiery, Nicolas M.   +3 more
core   +3 more sources

Linking Bipartiteness and Inversion in Algebra via Graph‐Theoretic Methods and Simulink

Complexity, Volume 2025, Issue 1, 2025.
Research for decades has concentrated on graphs of algebraic structures, which integrate algebra and combinatorics in an innovative way. The goal of this study is to characterize specific aspects of bipartite and inverse graphs that are associated with specific algebraic structures, such as weak inverse property quasigroups and their isotopes ...
Mohammad Mazyad Hazzazi, Muhammad Nadeem, Muhammad Kamran, Muhammad Arshad, M. I. Elashiry, Samuel Asefa Fufa, Marcin Mrugalski   +6 more
wiley   +1 more source

On the insertion of n-powers

, 2019
In algebraic terms, the insertion of $n$-powers in words may be modelled at the language level by considering the pseudovariety of ordered monoids defined by the inequality $1\le x^n$.
Almeida, J., Klíma, O.
core   +1 more source