Star products and central extensions
Jouko Mickelsson

TL;DR
This paper explores how algebra deformations can generate central extensions of loop groups and employs noncommutative geometry to regularize higher-dimensional current algebras for representation construction.
Contribution
It demonstrates the use of algebra deformations for central extensions and applies noncommutative geometry to regularize and represent higher-dimensional current algebras.
Findings
Deformations of smooth function algebras produce nontrivial central extensions of loop groups.
Noncommutative geometry can regularize higher-dimensional current algebras.
Framework for constructing representations of current algebras in higher dimensions.
Abstract
The purpose of the present note is two-fold. First, to show that deformations of algebras of smooth functions can be used to construct topologically nontrivial standard central extensions of loop groups. Second, to use noncommutative geometry as a regularization of current algebras in higher dimensions with the aim of constructing representations of current algebras.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Advanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology
