Canonical Cellular Decomposition for 𝒥-Irreducible Monoids

DOI10.1080/00927870902865852zbMath1197.20054OpenAlexW2159350360MaRDI QIDQ3406591

Lex E. Renner

Publication date: 19 February 2010

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

Full work available at URL: https://doi.org/10.1080/00927870902865852

zbMATH Keywords

cohomologyDynkin diagramsBetti numbersreductive monoidsrook monoidsBB-cellscellular decompositions\(\mathcal J\)-irreducible monoidssemisimple monoids\(B\times B\)-orbitsmonoid cellsrationally smooth monoids

Mathematics Subject Classification ID

Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Representation theory for linear algebraic groups (20G05) Group actions on varieties or schemes (quotients) (14L30) Algebraic monoids (20M32)

Related Items (2)

Betti Numbers of Toric Varieties and Eulerian Polynomials ⋮ The \(H\)-polynomial of an irreducible representation.

Cites Work

• Descent systems for Bruhat posets
• Analogue of the Bruhat decomposition for algebraic monoids
• Classification of semisimple varieties
• The system of idempotents and the lattice of \({\mathcal J}\)-classes of reductive algebraic monoids
• Linear algebraic monoids.
• Some theorems on actions of algebraic groups
• Rationally smooth algebraic monoids.
• The \(H\)-polynomial of a semisimple monoid.
• An Explicit Cell Decomposition of the Wonderful Compactification of a Semisimple Algebraic Group
• The Canonical Compactification of a Finite Group of Lie Type

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