On the fundamental representation of Borcherds algebras with one imaginary simple root

Details On the fundamental representation of Borcherds algebras with one imaginary simple root On the fundamental representation of Borcherds algebras with one imaginary simple root

1993-10-21

arxiv.org/abs/hep-th/9310139v1

Lett.Math.Phys. 31 (1994) 327-334

Physics

High Energy Physics

High Energy Physics - Theory

8 pages

Scientific paper

10.1007/BF00762796

Borcherds algebras represent a new class of Lie algebras which have almost all the properties that ordinary Kac-Moody algebras have, and the only major difference is that these generalized Kac-Moody algebras are allowed to have imaginary simple roots. The simplest nontrivial examples one can think of are those where one adds ``by hand'' one imaginary simple root to an ordinary Kac-Moody algebra. We study the fundamental representation of this class of examples and prove that an irreducible module is given by the full tensor algebra over some integrable highest weight module of the underlying Kac-Moody algebra. We also comment on possible realizations of these Lie algebras in physics as symmetry algebras in quantum field theory.

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