Generalized conformal realizations of Kac-Moody algebras

Journal Article · Thu Jan 15 04:00:00 EST 2009 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.3063628· OSTI ID:21175907

Palmkvist, Jakob ^[1]

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1. Albert-Einstein-Institut, Max-Planck-Institut fuer Gravitationsphysik, Am Muehlenberg, D-14476 Golm (Germany)

We present a construction which associates an infinite sequence of Kac-Moody algebras, labeled by a positive integer n, to one single Jordan algebra. For n=1, this reduces to the well known Kantor-Koecher-Tits construction. Our generalization utilizes a new relation between different generalized Jordan triple systems, together with their known connections to Jordan and Lie algebras. Applied to the Jordan algebra of Hermitian 3x3 matrices over the division algebras R, C, H, O, the construction gives the exceptional Lie algebras f{sub 4}, e{sub 6}, e{sub 7}, e{sub 8} for n=2. Moreover, we obtain their infinite-dimensional extensions for n{>=}3. In the case of 2x2 matrices, the resulting Lie algebras are of the form so(p+n,q+n) and the concomitant nonlinear realization generalizes the conformal transformations in a spacetime of signature (p,q)

• OSTI ID: 21175907
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 1 Vol. 50; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
HERMITIAN MATRIX
LIE GROUPS
NONLINEAR PROBLEMS
SPACE-TIME
TRANSFORMATIONS