Towards an operator algebraic construction of quantum field theories on de Sitter ...
Vertex constructions in representation theory of infinite dimensional Lie algebra.
Representations of hyper loop algebras and equivariant map algebras
Grant number: | 18/07593-0 |
Support Opportunities: | Scholarships abroad - Research |
Start date: | August 01, 2018 |
End date: | April 08, 2019 |
Field of knowledge: | Physical Sciences and Mathematics - Mathematics - Algebra |
Principal Investigator: | Renato Alessandro Martins |
Grantee: | Renato Alessandro Martins |
Host Investigator: | Ben Lewis Cox |
Host Institution: | Instituto de Ciência e Tecnologia (ICT). Universidade Federal de São Paulo (UNIFESP). Campus São José dos Campos. São José dos Campos , SP, Brazil |
Institution abroad: | 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. (AU) | |
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