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  Subalgebras of Hyperbolic Kac-Moody Algebras

Feingold, A. J., & Nicolai, H. (2004). Subalgebras of Hyperbolic Kac-Moody Algebras. In N. Sthanumoorthy, & K. Misra (Eds.), Kac-Moody Lie Algebras and Related Topics (pp. 97-114).

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-5099-9 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-509A-7
Genre: Conference Paper

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50991.pdf (Preprint), 247KB
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 Creators:
Feingold, Alex J., Author
Nicolai, Hermann1, Author              
Affiliations:
1Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24014              

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 Abstract: The hyperbolic (and more generally, Lorentzian) Kac-Moody (KM) Lie algebras A of rank r+2 > 2 are shown to have a rich structure of indefinite KM subalgebras which can be described by specifying a subset of positive real roots of A such that the difference of any two is not a root of A. Taking these as the simple roots of the subalgebra gives a Cartan matrix, generators and relations for the subalgebra. Applying this to the canonical example of a rank 3 hyperbolic KM algebra, F, we find that F contains all of the simply laced rank 2 hyperbolics, as well as an infinite series of indefinite KM subalgebras of rank 3. It is shown that A also contains Borcherds algebras, obtained by taking all of the root spaces of A whose roots are in a hyperplane (or any proper subspace). This applies as well to the case of rank 2 hyperbolics, where the Borcherds algebras have all their roots on a line, giving the simplest possible examples.

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Language(s): eng - English
 Dates: 2004
 Publication Status: Published in print
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 Identifiers: eDoc: 50991
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Title: Ramanujan International Symposium on Kac-Moody Lie Algebras and Applications
Place of Event: Chennai, India
Start-/End Date: 2002-01-28 - 2002-01-31

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Source 1

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Title: Kac-Moody Lie Algebras and Related Topics
Source Genre: Proceedings
 Creator(s):
Sthanumoorthy, N., Editor
Misra, K., Editor
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Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 97 - 114 Identifier: -

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Title: Contemporary Mathematics
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Pages: - Volume / Issue: 343 Sequence Number: - Start / End Page: - Identifier: -