Analogue of the Bruhat-Chevalley order for reductive monoids

DOI10.1006/jabr.1997.7111zbMath0891.20039OpenAlexW1966748992MaRDI QIDQ1372631

Edwin A. Pennell, Lex E. Renner, Putcha, Mohan S.

Publication date: 19 July 1998

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

Full work available at URL: https://doi.org/10.1006/jabr.1997.7111

zbMATH Keywords

Weyl groupsaffine algebraic varietiesalgebraic monoidsreductive monoidsBruhat decompositionsBruhat-Chevalley ordersreductive unit groups

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) Semigroups of transformations, relations, partitions, etc. (20M20) Regular semigroups (20M17) Inverse semigroups (20M18)

Related Items (28)

R-POLYNOMIALS OF FINITE MONOIDS OF LIE TYPE ⋮ Extending the Bruhat order and the length function from the Weyl group to the Weyl monoid. ⋮ Big cells and LU factorization in reductive monoids ⋮ Asymptotic semigroups and two-sided weak orders ⋮ Stirling posets ⋮ Remarks on enveloping semigroups ⋮ Sects ⋮ Algebraic Monoids and Renner Monoids ⋮ Conjugacy Decomposition of Canonical and Dual Canonical Monoids ⋮ On the Borel submonoid of a symplectic monoid ⋮ THE BRAID ROOK MONOID ⋮ Nilpotent variety of a reductive monoid. ⋮ Generic Hecke algebra for Renner monoids. ⋮ ROOT SEMIGROUPS IN REDUCTIVE MONOIDS ⋮ Incidence monoids: automorphisms and complexity ⋮ Monoid Hecke algebras ⋮ Shellability in reductive monoids ⋮ Bruhat-Chevalley order in reductive monoids. ⋮ THE RENNER MONOIDS AND CELL DECOMPOSITIONS OF THE SYMPLECTIC ALGEBRAIC MONOIDS ⋮ The Maximal Chains of the Extended Bruhat Orders on the  × -Orbits of an Infinite Renner Monoid ⋮ PRESENTATION FOR RENNER MONOIDS ⋮ Bruhat-Chevalley order on \(\mathcal J\)-classes of reductive monoids. ⋮ The rook monoid is lexicographically shellable ⋮ Weak order on complete quadrics ⋮ Conjugacy decomposition of reductive monoids. ⋮ PARABOLIC MONOIDS I: STRUCTURE ⋮ FINE BRUHAT INTERSECTIONS FOR REDUCTIVE MONOIDS ⋮ Rational smoothness and fixed points of torus actions

Cites Work

• The Bruhat decomposition, Tits system and Iwahori ring for the monoid of matrices over a finite field
• On some geometric aspects of Bruhat orderings. I: A finer decomposition of Bruhat cells
• Analogue of the Bruhat decomposition for algebraic monoids
• The system of idempotents and the lattice of \({\mathcal J}\)-classes of reductive algebraic monoids
• Buildings of spherical type and finite BN-pairs
• Analogue of the Bruhat decomposition for algebraic monoids. II: The length function and the trichotomy
• Classification of Semisimple Algebraic Monoids
• Désingularisation des variétés de Schubert généralisées
• Sandwich Matrices, Solomon Algebras, and Kazhdan-Lusztig Polynomials
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