Simplicity of augmentation submodules for transformation monoids

DOI10.1007/s10468-020-09977-7zbMath1496.20124arXiv1804.10943OpenAlexW3041025055MaRDI QIDQ2042297

Benjamin Steinberg, M. H. Shahzamanian

Publication date: 28 July 2021

Published in: Algebras and Representation Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1804.10943

zbMATH Keywords

simplicial complexessimple modulesposetsgraphstransformation monoidsmonoid representation theory

Mathematics Subject Classification ID

Semigroups of transformations, relations, partitions, etc. (20M20) Semigroup rings, multiplicative semigroups of rings (20M25) Representation of semigroups; actions of semigroups on sets (20M30)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The global dimension of the full transformation monoid (with an appendix by V. Mazorchuk and B. Steinberg)
• Representation theory of finite monoids
• Eigenvectors for a random walk on a left-regular band
• Primitive orthogonal idempotents for \(R\)-trivial monoids.
• The quiver of an algebra associated to the Mantaci-Reutenauer descent algebra and the homology of regular semigroups.
• A theory of transformation monoids: combinatorics and representation theory
• A combinatorial formula for orthogonal idempotents in the 0-Hecke algebra of the symmetric group.
• Edge flipping in graphs
• On the representation theory of finite \(J\)-trivial monoids
• The Černý conjecture for one-cluster automata with prime length cycle
• The representation theory of the monoid of all partial functions on a set and related monoids as EI-category algebras.
• Combinatorial topology and the global dimension of algebras arising in combinatorics
• Language and automata theory and applications. Second international conference, LATA 2008, Tarragona, Spain, March 13--19, 2008. Revised papers
• On the quiver of the descent algebra.
• Fast Fourier transforms for finite inverse semigroups
• A semigroup approach to wreath-product extensions of Solomon's descent algebras.
• Complex representations of finite monoids. II: Highest weight categories and quivers
• Random walks and hyperplane arrangements
• Synchronizing finite automata on Eulerian digraphs.
• Semigroups, rings, and Markov chains
• Representations of the rook monoid.
• A combinatorial description of the spectrum for the Tsetlin library and its generalization to hyperplane arrangements
• Random walks on rings and modules
• Combinatorial Markov chains on linear extensions
• Inverse semigroup spectral analysis for partially ranked data
• Algebraic topology of finite topological spaces and applications
• Directed nonabelian sandpile models on trees
• Between primitive and 2-transitive: synchronization and its friends
• Synchronizing groups and automata
• On the structure of semigroups
• Graph Theory
• COMPLETELY REDUCIBLE SETS
• The classification of almost simple $\tfrac {3}{2}$-transitive groups
• THE AVERAGING TRICK AND THE ČERNÝ CONJECTURE
• A QUADRATIC UPPER BOUND ON THE SIZE OF A SYNCHRONIZING WORD IN ONE-CLUSTER AUTOMATA
• Quivers of monoids with basic algebras
• THE QUIVER OF THE SEMIGROUP ALGEBRA OF A LEFT REGULAR BAND
• Random Walks, Arrangements, Cell Complexes, Greedoids, and Self-Organizing Libraries
• Fast Fourier transforms for the rook monoid
• Markov chains, ${\mathscr R}$-trivial monoids and representation theory
• Permutation representations and rational irreducibility
• The Face Semigroup Algebra of a Hyperplane Arrangement

This page was built for publication: Simplicity of augmentation submodules for transformation monoids