Title

Weyl Groups of some Hyperbolic Kac-Moody Algebras

Authors

Alex J. Feingold, Binghamton University--SUNYFollow
Daniel Vallières

Document Type

Article

Publication Date

1-2016

Keywords

Group Theory, Rings and Algebras, Representation Theory

Abstract

We use the theory of Clifford algebras and Vahlen groups to study Weyl groups of hyperbolic Kac-Moody algebras T ++ n , obtained by a process of double extension from a Cartan matrix of finite type Tn, whose corresponding generalized Cartan matrices are symmetric.

Comments

Contents

• Introduction
• Generalities on orthogonal geometries
• Clifford algebras, Pin and Spin groups
• The Clifford group
• Abstract Pin and Spin groups
• Pin and Spin groups
• Lorentzian geometry over R
• Change of fields
• Vahlen groups
• Vahlen groups
• Change of fields
• Generalized Cartan matrices, system of simple roots and Weyl groups
• A useful normalization
• Canonical Lorentzian extensions
• Change of fields
• Weyl groups of the hyperbolic canonical Lorentzian extensions T ++ n with symmetric Cartan matrices
• Spinor norm of outer autormorphisms
• Connections with previous descriptions of the Weyl group
• Paravectors
• Vahlen groups for paravectors
• Hermitian matrices
• References

Recommended Citation

Feingold, A. J., & Vallières, D. (2016). Weyl groups of some hyperbolic Kac-Moody algebras. arXiv preprint arXiv:1601.04117.