Clusterization of Correlation Functions

Zuevsky, Alexander

doi:10.1007/978-3-319-51718-6_28

Groups, Modules, and Model Theory - Surveys and Recent Developments 2017

DOI: 10.1007/978-3-319-51718-6_28

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Clusterization of Correlation Functions

Alexander Zuevsky

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2023

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Reduction cohomology of Riemann surfaces

Zuevsky

2023

Rev. Math. Phys.

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We study the algebraic conditions leading to the chain property of complexes for vertex operator algebra [Formula: see text]-point functions (with their convergence assumed) with differential being defined through reduction formulas. The notion of the reduction cohomology of Riemann surfaces is introduced. Algebraic, geometrical, and cohomological meanings of reduction formulas are clarified. A counterpart of the Bott–Segal theorem for Riemann surfaces in terms of the reductions cohomology is proven. It is shown that the reduction cohomology is given by the cohomology of [Formula: see text]-point connections over the vertex operator algebra bundle defined on a genus [Formula: see text] Riemann surface [Formula: see text]. The reduction cohomology for a vertex operator algebra with formal parameters identified with local coordinates around marked points on [Formula: see text] is found in terms of the space of analytical continuations of solutions to Knizhnik–Zamolodchikov equations. For the reduction cohomology, the Euler–Poincaré formula is derived. Examples for various genera and vertex operator cluster algebras are provided.

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Reduction cohomology of Riemann surfaces

Zuevsky

2023

Rev. Math. Phys.

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Clusterization of Correlation Functions

Cited by 1 publication

References 7 publications

Reduction cohomology of Riemann surfaces

Reduction cohomology of Riemann surfaces

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