Vol. 10, No. 1, 2020

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ChevLie: Constructing Lie algebras and Chevalley groups

Meinolf Geck

Vol. 10 (2020), 41–49
DOI: 10.2140/jsag.2020.10.41
Abstract

We present ChevLie-1.1, a module for Julia and, ultimately, the emerging OSCAR system. It provides functions for constructing simple Lie algebras and the corresponding Chevalley groups (of adjoint or other types), using a recently established approach via Lusztig’s “canonical bases”. These programs, combined with the Julia interface to SINGULAR, supply an efficient, user-friendly way to establish a key part of a new characterisation of Lusztig’s “special” nilpotent orbits in simple Lie algebras.

Keywords
Lie algebras, canonical bases, weighted Dynkin diagrams
Mathematical Subject Classification 2010
Primary: 20G40
Secondary: 17B45
Supplementary material

A Julia module for constructing Lie algebras and Chevalley groups

Milestones
Received: 13 January 2020
Revised: 17 March 2020
Accepted: 21 April 2020
Published: 2 May 2020
Authors
Meinolf Geck
IAZ – Lehrstuhl für Algebra
Universität Stuttgart
Stuttgart
Germany