Weyl groups of some hyperbolic Kac-Moody algebras

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 T_n, whose corresponding generalized Cartan matrices are symmetric.

30 pages; Minor corrections from referee; Final version for publication; PARI program and explanatory Readme.txt file used in proof of Theorem 6.5 are available from the authors, may be available as ancillary files

References in corpus (2)

• Classification of hyperbolic Dynkin diagrams, root lengths and Weyl group orbits
• Hyperbolic Weyl groups and the four normed division algebras