Idempotent lattices, Renner monoids and cross section lattices of the special orthogonal algebraic monoids.

DOI10.1016/J.JALGEBRA.2002.08.001zbMath1043.20043OpenAlexW2031397968MaRDI QIDQ1421782

Zhenheng Li

Publication date: 3 February 2004

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2002.08.001

zbMATH Keywords

Weyl groupsspecial orthogonal groupslinear algebraic monoidsRenner monoidsadmissible subsetscross-section latticesreductive algebraic monoidsidempotent latticesspecial orthogonal algebraic monoids

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) Semigroups of transformations, relations, partitions, etc. (20M20)

Related Items (12)

The orbits of generalized orthogonal monoids under the action of their unit groups ⋮ Orbit decompositions of orthogonal monoids and the orders of finite orthogonal monoids ⋮ Infinite-dimensional reductive monoids associated to highest weight representations of Kac-Moody groups ⋮ Algebraic Monoids and Renner Monoids ⋮ Partial symmetry, reflection monoids and Coxeter groups. ⋮ Orders of the Renner monoids. ⋮ Enumeration of symplectic and orthogonal injective partial transformations. ⋮ Modules for order preserving symplectic and even special orthogonal rook monoids ⋮ PRESENTATION FOR RENNER MONOIDS ⋮ Generating sets in orthogonal and symplectic rook monoids ⋮ The Symplectic Monoid ⋮ Various Forms of Generating Subsemigroups in Algebraic Monoids

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