Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Classification of semisimple algebraic monoids
HTML articles powered by AMS MathViewer

by Lex E. Renner PDF
Trans. Amer. Math. Soc. 292 (1985), 193-223 Request permission

Abstract:

Let $X$ be a semisimple algebraic monoid with unit group $G$. Associated with $E$ is its polyhedral root system $(X,\Phi ,C)$, where $X = X(T)$ is the character group of the maximal torus $T \subseteq G$, $\Phi \subseteq X(T)$ is the set of roots, and $C = X(\overline T )$ is the character monoid of $\overline T \subseteq E$ (Zariski closure). The correspondence $E \to (X,\Phi ,C)$ is a complete and discriminating invariant of the semisimple monoid $E$, extending the well-known classification of semisimple groups. In establishing this result, monoids with preassigned root data are first constructed from linear representations of $G$. That done, we then show that any other semisimple monoid must be isomorphic to one of those constructed. To do this we devise an extension principle based on a monoid analogue of the big cell construction of algebraic group theory. This, ultimately, yields the desired conclusions.
References
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 14M99, 20M99
  • Retrieve articles in all journals with MSC: 14M99, 20M99
Additional Information
  • © Copyright 1985 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 292 (1985), 193-223
  • MSC: Primary 14M99; Secondary 20M99
  • DOI: https://doi.org/10.1090/S0002-9947-1985-0805960-9
  • MathSciNet review: 805960