Khudaverdian H. Non-linear homomorphisms of algebras of functions are induced by thick morphisms (abstract)

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Speaker: Hovhannes Khudaverdian

Title: Non-linear homomorphisms of algebras of functions are induced by thick morphisms

Abstract:
In 2014 Th. Voronov introduced the notion of thick morphisms of (super)manifolds as a tool for constructing [math]\displaystyle{ L_{\infty} }[/math]-morphisms of homotopy Poisson algebras. Thick morphisms generalise ordinary smooth maps, but are not maps themselves. Nevertheless, they induce pull-backs on [math]\displaystyle{ C^{\infty} }[/math] functions. These pull-backs are in general non-linear maps between the algebras of functions which are so-called "non-linear homomorphisms". By definition, this means that their differentials are algebra homomorphisms in the usual sense. The following conjecture was formulated: an arbitrary non-linear homomorphism of algebras of smooth functions is generated by some thick morphism. We prove here this conjecture in the class of formal functionals.


Event: Diffieties, Cohomological Physics, and Other Animals, 13-17 December 2021, Moscow.
Alexandre Vinogradov Memorial Conference.