The system of idempotents and the lattice of \({\mathcal J}\)-classes of reductive algebraic monoids

DOI10.1016/0021-8693(88)90225-6zbMath0678.20039OpenAlexW1970957731MaRDI QIDQ1123982

Lex E. Renner, Putcha, Mohan S.

Publication date: 1988

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-8693(88)90225-6

zbMATH Keywords

idempotentsirreducible representationsunit groupTits buildinglattice of \({\mathcal J}\)-classesregular algebraic monoid

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) Semigroups of transformations, relations, partitions, etc. (20M20) Representation theory for linear algebraic groups (20G05)

Related Items (54)

MONOIDS WITH IDEMPOTENT CROSS-SECTIONS ⋮ The Canonical Compactification of a Finite Group of Lie Type ⋮ A generic algebra associated to certain Hecke algebras. ⋮ Betti Numbers of Toric Varieties and Eulerian Polynomials ⋮ Cell Decompositions of the Special Orthogonal Algebraic Monoids ⋮ Descent systems for Bruhat posets ⋮ The blocks of solvable algebraic monoids ⋮ The lattice of \(\mathcal J\)-classes of \(({\mathcal J},\sigma)\)-irreducible monoids ⋮ Generalised Tits alternative for linear semigroups ⋮ Centralizer of an idempotent in a reductive monoid ⋮ Triangularizable semigroups of matrices ⋮ Rationally smooth algebraic monoids. ⋮ Analogue of the Bruhat-Chevalley order for reductive monoids ⋮ Classification of semisimple varieties ⋮ Linear semigroups of polynomial growth in positive characteristic ⋮ Infinite-dimensional reductive monoids associated to highest weight representations of Kac-Moody groups ⋮ Standard parabolic subsets of highest weight modules ⋮ Remarks on enveloping semigroups ⋮ Algebraic Monoids and Renner Monoids ⋮ The Betti Numbers of Simple Embeddings ⋮ Irreducible representations of semisimple algebraic groups and supersolvable lattices. ⋮ Transitive maps from posets to Dynkin diagrams ⋮ The \(H\)-polynomial of an irreducible representation. ⋮ Idempotent lattices, Renner monoids and cross section lattices of the special orthogonal algebraic monoids. ⋮ Nilpotent variety of a reductive monoid. ⋮ Parabolic subgroups and algebraic monoids. ⋮ The local semilattices of chains of idempotents ⋮ Equivariant cohomology of rationally smooth group embeddings ⋮ Monoid Hecke algebras ⋮ The \(H\)-polynomial of a semisimple monoid. ⋮ Möbius functions and semigroup representation theory. II: Character formulas and multiplicities. ⋮ Sandwich Matrices, Solomon Algebras, and Kazhdan-Lusztig Polynomials ⋮ Invariant convex subcones of the Tits cone of a linear Coxeter group ⋮ On the blocks of semisimple algebraic groups and associated generalized Schur algebras. ⋮ Shellability in reductive monoids ⋮ Semigroup algebras of linear semigroups ⋮ Bruhat-Chevalley order in reductive monoids. ⋮ Stable reductive varieties. I: Affine varieties ⋮ THE RENNER MONOIDS AND CELL DECOMPOSITIONS OF THE SYMPLECTIC ALGEBRAIC MONOIDS ⋮ Observable subgroups of algebraic monoids. ⋮ Orders of the Renner monoids. ⋮ The Maximal Chains of the Extended Bruhat Orders on the  × -Orbits of an Infinite Renner Monoid ⋮ PRESENTATION FOR RENNER MONOIDS ⋮ Types of reductive monoids ⋮ The lattice of \(\mathcal J\)-classes of \(({\mathcal J},\sigma)\)-irreducible monoids. II ⋮ Products of idempotents in algebraic monoids ⋮ Monoids on groups with BN-pairs ⋮ Canonical semigroups. ⋮ The monoid generated by projections in an algebraic group ⋮ Möbius function on cross-section lattices. ⋮ Canonical Cellular Decomposition for 𝒥-Irreducible Monoids ⋮ The classification of (J, σ)-irreducible monoids of typeA₄ ⋮ Modular representations of finite monoids of Lie type ⋮ The Orbit Structures of (, σ)-Irreducible Monoids

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