# 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 [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.*