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

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 $L_{\mathrm{\infty }}$-morphisms of homotopy Poisson algebras. Thick morphisms generalise ordinary smooth maps, but are not maps themselves. Nevertheless, they induce pull-backs on $C^{\mathrm{\infty }}$ 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.