Lex Renner

    Lex E. Renner

    Professor
    Ph.D., University of British Columbia, 1982

    Current research interests


Telephone: 519-661-2111 ext 86515
Fax: 519-661-3610

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Course Information(2014-2015)

Math 3121A COURSE OUTLINE

Math 4123A COURSE OUTLINE

Math 9141B COURSE OUTLINE


ESCUTCHEON

Renner is known for his work on algebraic monoids, a branch of algebra (MSC(2010):20M32) that he developed starting around 1979. His creative academic background has forged a unique perspective combining geometry and groups with convexity and semigroups. He and M.S. Putcha (North Carolina State) have authored nearly two hundred papers on algebraic monoids and related topics.

The theory of algebraic monoids is a natural synthesis of algebraic group theory (Chevalley, Borel, Tits) and torus embeddings (Mumford, Kempf, et al). The resulting theory is a significant part of the theory of spherical embeddings (Brion, Luna, Vust). Horospherical varieties (Popov, Vinberg) were a significant catalyst in the development. Related work on symmetric varieties was motivated by classical enumerative problems (De Concini, Procesi).

Renner's contribution contains results on the following issues.

Renner has authored a monograph entitled "Linear Algebraic Monoids". The intention of this monograph is to convince the reader that reductive monoids are among the darlings of mathematics. He does this by systematically assembling many of the major known results, with many proofs, examples, explanations, exercises and open problems.

LINEAR ALGEBRAIC MONOIDS
Encyclopedia of Mathematical Sciences 134
Invariant Theory V
Springer-Verlag, 2005.
Contents: *Background *Algebraic Monoids *Regularity Conditions *Classification *Universal Constructions *Orbit Structure *Analogue of the Bruhat Decomposition *Representations and Blocks *Monoids of Lie Type *Cellular Decompositions *Conjugacy Classes *Centralizer of a Semisimple Element *Combinatorics Related to Algebraic Monoids *Survey of Related Developments.
Key notions: Reductive group, regular monoid, diagonal idempotent, blocks and representations, highest weight category, monoid Bruhat decomposition, centralizer, divisor class group, adjoint quotient, flat deformation, generalized Schubert cell, reductive monoid as spherical variety.

Last update: August 21, 2014