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Rank 2 symmetric hyperbolic Kac-Moody algebras
- Source :
- Nagoya Mathematical Journal. 140:41-75
- Publication Year :
- 1995
- Publisher :
- Cambridge University Press (CUP), 1995.
-
Abstract
- Affine Kac-Moody algebras represent a well-trodden and well-understood littoral beyond which stretches the vast, chaotic, and poorly-understood ocean of indefinite Kac-Moody algebras. The simplest indefinite Kac-Moody algebras are the rank 2 Kac-Moody algebras (a) (a ≥ 3) with symmetric Cartan matrix , which form part of the class known as hyperbolic Kac-Moody algebras. In this paper, we probe deeply into the structure of those algebras (a), the e. coli of indefinite Kac-Moody algebras. Using Berman-Moody’s formula ([BM]), we derive a purely combinatorial closed form formula for the root multiplicities of the algebra (a), and illustrate some of the rich relationships that exist among root multiplicities, both within a single algebra and between different algebras in the class. We also give an explicit description of the root system of the algebra (a). As a by-product, we obtain a simple algorithm to find the integral points on certain hyperbolas.
- Subjects :
- Discrete mathematics
Symmetric algebra
Pure mathematics
Class (set theory)
Jordan algebra
Rank (linear algebra)
010308 nuclear & particles physics
General Mathematics
010102 general mathematics
Structure (category theory)
01 natural sciences
0103 physical sciences
Cartan matrix
Algebra representation
Cellular algebra
0101 mathematics
Mathematics
Subjects
Details
- ISSN :
- 21526842 and 00277630
- Volume :
- 140
- Database :
- OpenAIRE
- Journal :
- Nagoya Mathematical Journal
- Accession number :
- edsair.doi...........01d631728081be1087dd129d0022acef