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Abstract:
We will introduce a new cohomology theory that extends
H. Cartan's cohomology
theory of G^* algebras.
The latter is an algebraic abstraction of the topological equivariant
cohomology theory for G spaces, where G is a compact Lie group. Cartan's
theory, discovered in the 50s and further developed by others in the 90s,
gave a de Rham model for the topological equivariant cohomology, the same way
ordinary de Rham theory does for singular cohomology in a geometric setting.
Chiral equivariant cohomology is one that takes values in a vertex algebra
and includes Cartan's cohomology as a subalgebra. I will give a brief
introduction to vertex algebra, and then discuss the construction of the new
cohomology and some of the basic results and examples.
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