𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Hecke Algebras and Semisimplicity of Monoid Algebras

✍ Scribed by Mohan S Putcha

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
140 KB
Volume
218
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

✦ Synopsis

We begin by constructing Hecke algebras for arbitrary finite regular monoids M. We then show that the semisimplicity of the complex monoid algebra ‫ރ‬ M is equivalent to the semisimplicity of the associated Hecke algebras and a condition on induced group characters. We apply these results to finite Lie-type monoids M. We show that the monoid algebra FM over a field F is semisimple if and only if the characteristic of F does not divide the order of the unit group G. This is accomplished by developing formulas for the unities of ‫ރ‬ J, J a J J-class of M. The unity is explicitly given when G is a simply connected Chevalley group and J is associated with a Borel subgroup of G.

📜 SIMILAR VOLUMES

Semisimplicity of Parabolic Hecke Algebr
Semisimplicity of Parabolic Hecke Algebras
✍ Yasushi Gomi 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 212 KB

The semisimplicity of Iwahori᎐Hecke algebras has been studied by several Ž . authors. A. Gyoja J. Algebra 174, 1995, 553᎐572 gave a necessary and sufficient condition for Iwahori᎐Hecke algebras to be semisimple, using the modular repre-Ž . sentation theory. The author J. Algebra 183, 1996, 514᎐544 s

André–Quillen Cohomology of Monoid Algeb
André–Quillen Cohomology of Monoid Algebras
✍ Klaus Altmann; Arne B. Sletsjøe 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 101 KB

The best results are obtained either in the general case for the first three cohomology groups, or in the case of isolated singularities for all cohomology groups, respectively.

Residue Construction of Hecke Algebras
Residue Construction of Hecke Algebras
✍ Victor Ginzburg; Mikhail Kapranov; Eric Vasserot 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 393 KB

Hecke algebras are usually defined algebraically, via generators and relations. We give a new algebra-geometric construction of affine and double-affine Hecke algebras (the former is known as the Iwahori Hecke algebra, and the latter was introduced by Cherednik) in terms of residues. More generally,

A Duality for Modules over Monoidal Cate
A Duality for Modules over Monoidal Categories of Representations of Semisimple Hopf Algebras
✍ D Tambara 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 285 KB

For a finite dimensional semisimple cosemisimple Hopf algebra A and its dual Hopf algebra B, we set up a natural one-to-one correspondence between categories with actions of the monoidal categories of representations of A and of B. This gives a categorical interpretation of the duality for actions o

Semisimplicity of adjacency algebras of
Semisimplicity of adjacency algebras of association schemes
✍ Akihide Hanaki 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 69 KB

In this paper, we investigate the semisimplicity of adjacency algebras of association schemes over positive characteristic fields. Our main result is that the Frame number characterizes semisimplicity of an adjacency algebra. In a sense, this is a generalization of Maschke's theorem.