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3-point Virasoro algebra action on free field realization and gerbes

Grant number: 18/07593-0
Support type:Scholarships abroad - Research
Effective date (Start): August 01, 2018
Effective date (End): April 08, 2019
Field of knowledge:Physical Sciences and Mathematics - Mathematics
Principal Investigator:Renato Alessandro Martins
Grantee:Renato Alessandro Martins
Host: Ben Lewis Cox
Home Institution: Instituto de Ciência e Tecnologia (ICT). Universidade Federal de São Paulo (UNIFESP). Campus São José dos Campos. São José dos Campos , SP, Brazil
Local de pesquisa : College of Charleston, United States  
Associated research grant:14/09310-5 - Algebraic structures and their representations, AP.TEM

Abstract

The notion of a gerbe was introduced by Jean Giraud in 1971 in the context of algebraic geometry following ideas of Grothendieck. In a more differential geometric setting, this notion is introduced if one lets $\mathcal H$ be a complex Hilbert space and takes $PU(\mathcal H)$ to denote the projective unitary group $U(\mathcal H)/S^1$. Then a gerbe over a topological space $X$ is a principal $PU(\mathcal H)$-bundle over $X$. The topological classification of gerbes over $X$ is given by the third integral cohomology group $H^3(X,\mathbb Z)$ and when $X$ is a topological group, this integral cohomology group can be related to the locally continuous third cohomology group of $X$. This is the object of study in the project under review but in the context of representation theory of Krichever-Novikov algebras.