Reduction cohomology of Riemann surfaces

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F23%3A00575120" target="_blank" >RIV/67985840:_____/23:00575120 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1142/S0129055X23300054" target="_blank" >https://doi.org/10.1142/S0129055X23300054</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1142/S0129055X23300054" target="_blank" >10.1142/S0129055X23300054</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Reduction cohomology of Riemann surfaces

Popis výsledku v původním jazyce

We study the algebraic conditions leading to the chain property of complexes for vertex operator algebra n-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 n-point connections over the vertex operator algebra bundle defined on a genus g Riemann surface S-(g). The reduction cohomology for a vertex operator algebra with formal parameters identified with local coordinates around marked points on S-(g) is found in terms of the space of analytical continuations of solutions to Knizhnik-Zamolodchikov equations. For the reduction cohomology, the Euler-Poincare formula is derived. Examples for various genera and vertex operator cluster algebras are provided.

Název v anglickém jazyce

Reduction cohomology of Riemann surfaces

Popis výsledku anglicky

We study the algebraic conditions leading to the chain property of complexes for vertex operator algebra n-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 n-point connections over the vertex operator algebra bundle defined on a genus g Riemann surface S-(g). The reduction cohomology for a vertex operator algebra with formal parameters identified with local coordinates around marked points on S-(g) is found in terms of the space of analytical continuations of solutions to Knizhnik-Zamolodchikov equations. For the reduction cohomology, the Euler-Poincare formula is derived. Examples for various genera and vertex operator cluster algebras are provided.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Reviews in Mathematical Physics

ISSN

0129-055X

e-ISSN

1793-6659

Svazek periodika

35

Číslo periodika v rámci svazku

7

Stát vydavatele periodika

SG - Singapurská republika

Počet stran výsledku

32

Strana od-do

2330005

Kód UT WoS článku

000990052000001

EID výsledku v databázi Scopus

2-s2.0-85171766528