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Structure constants of Kac–Moody Lie algebras

  • Bill CasselmanEmail author
Chapter
Part of the Progress in Mathematics book series (PM, volume 257)

Abstract

This paper outlines an algorithm for computing structure constants of Kac–Moody Lie algebras. In contrast to the methods currently used for finite-dimensional Lie algebras, which rely on the additive structure of the roots, it reduces to computations in the extended Weyl group first defined by Jacques Tits in about 1966. The new algorithm has some theoretical interest, and its basis is a mathematical result generalizing a theorem of Tits about the finite-dimensional case. The explicit algorithm seems to be new, however, even in the finite-dimensional case. I include towards the end some remarks about repetitive patterns of structure constants, which I expect to play an important role in understanding the associated groups. That neither the idea of Tits nor the phenomenon of repetition has already been exploited I take as an indication of how little we know about Kac–Moody structures.

Keywords

Structure constants Kac–Moody Lie algebras 

Mathematics Subject Classification

17B05 17B22 17B45 17B67 

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Mathematics DepartmentUniversity of British ColumbiaVancouverCanada

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