Khudaverdian H. Non-linear homomorphisms of algebras of functions are induced by thick morphisms (abstract): Difference between revisions
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| title = Non-linear homomorphisms of algebras of functions are induced by thick morphisms | | 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>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>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. | | abstract = In 2014 Th. Voronov introduced the notion of thick morphisms of (super)manifolds as a tool for constructing <math>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>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. | ||
| video = https://video.gdeq. | | video = https://video.gdeq.org/AMV-conf-20211213-Hovhannes_Khudaverdian.mp4 | ||
| slides = [[Media:KhudaverdianAMVconf2021slides.pdf|KhudaverdianAMVconf2021slides]] | | slides = [[Media:KhudaverdianAMVconf2021slides.pdf|KhudaverdianAMVconf2021slides]] | ||
| references = | | references = | ||
Latest revision as of 08:38, 4 January 2025
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 -morphisms of homotopy Poisson algebras. Thick morphisms generalise ordinary smooth maps, but are not maps themselves. Nevertheless, they induce pull-backs on 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.
Video
Slides: KhudaverdianAMVconf2021slides
Event: Diffieties, Cohomological Physics, and Other Animals, 13-17 December 2021, Moscow.
Alexandre Vinogradov Memorial Conference.