Geometry of the Frenkel-Kac-Segal cocycle

Details Geometry of the Frenkel-Kac-Segal cocycle Geometry of the Frenkel-Kac-Segal cocycle

1994-04-12

arxiv.org/abs/hep-th/9404062v1

Physics

High Energy Physics

High Energy Physics - Theory

26 pages

Scientific paper

We present an analysis of the cocycle appearing in the vertex operator representation of simply-laced, affine, Kac-Moody algebras. We prove that it can be described in the context of $R$-commutative geometry, where $R$ is a Yang-Baxter operator, as a strong $R$-commutative algebra. We comment on the Hochschild, cyclic and dihedral homology theories that appear in non-commutative geometry and their potential relation to string theory.

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