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Cohomology in algebra, geometry, physicsand statistics
Multiple sewn cohomology for vertex algebras
Speaker’s name:
Sasha Zuevsky
Speaker’s affiliation:
IM, CAS, Praha
Place:
seminar room Konirna in IM front building, ground floor
Date:
Wednesday, 4. December 2019 - 11:30 to 12:30
Abstract:
In 2010 Y.Z. Huang has introduced the notion of a cohomology of grading-restricted vertex algebras. The main construction of coboundary operator was given using considerations of rational functions obtained as matrix elements for such vertex algebras. As we know from the theory of correlation functions for vertex algebras, matrix elements correspond to the choice of formal parameters for vertex operators to be local coordinates on the complex sphere. One can consider more complicated situation when local coordinates for vertex operators are taken on a complex sphere sewn to itself. This procedure would change coboundary operators and enrich the cohomological structure of corresponding vertex algebras. In this lecture we introduce the cohomology associated to multiple g-handle sewn to complex sphere and defining coboundary operators by summation of matrix elements with intertwining operators inserted.