Virasoro extensions for diffeomorphisms with breaks
Anton Izosimov, Boris Khesin, Howard Xiao

TL;DR
This paper constructs a new class of central extensions for broken diffeomorphisms on the circle, generalizing the Virasoro algebra to include singularities at finite points.
Contribution
It introduces explicit n-dimensional central extensions of the groupoid of broken circle diffeomorphisms and their algebroids, extending the classical Virasoro structure.
Findings
Constructed a nontrivial n-dimensional central extension of the broken diffeomorphism groupoid.
Extended the Virasoro algebra to a setting with finite break points.
Analyzed related extensions on an interval with fixed or variable endpoints.
Abstract
We study homeomorphisms of the circle that are smooth diffeomorphisms away from a finite set of points. These "broken diffeomorphisms" do not form a Lie group, but instead naturally assemble into a Lie groupoid. We construct an explicit nontrivial -dimensional central extension of this groupoid, which restricts to the classical Virasoro group when confined to smooth diffeomorphisms. We further describe the associated "broken Virasoro" algebroid, defined as a nontrivial -dimensional central extension of the Lie algebroid of vector fields on the circle that are smooth except at points. This construction generalizes the Virasoro algebra. As a byproduct, we analyze a related setting on an interval: we construct a nontrivial central extension of the Lie algebra of vector fields vanishing at the endpoints, together with the corresponding central extension of the group of…
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