Geometry of the Frenkel-Kac-Segal cocycle

1994/04/12 by Nikolaos Kalogeropoulos, Kalogeropoulos, Nikolaos
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Algebra (math.QA) #hep-th #math.QA

paper · pdf · doi:10.48550/arxiv.hep-th/9404062

26 pages

arxiv created 1994/04/12 · openalex publication_date 1994/04/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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