Work

Canonical structure constants for simple Lie algebras

Year: 2024

Type: article

Abstract: Let $$\mathfrak {g}$$ g be a finite-dimensional simple Lie algebra over $$\mathbb {C}$$ C . In the 1950s Chevalley showed that $$\mathfrak {g}$$ g admits particular bases, now called “Chevalley bases”, for which the corresponding structure constants are integers. Such bases are not unique but, using Lusztig’s theory of canonical bases, one can single out a “canonical” Chevalley basis which is unique up to a global sign. In this paper, we give explicit formulae for the structure constants with respect to such a basis.

Source: Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry

DOI: 10.1007/s13366-024-00767-6

Authors: Meinolf Geck, Alexander Lang

Institution: University of Stuttgart

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: Deutsche Forschungsgemeinschaft, Universität Stuttgart