Deformations of the exterior algebra of differential forms

Let D: Ω → Ω be a differential operator defined in the exterior algebra Ω of differential forms over the polynomial ring S in n variables. In this work we give conditions for deforming the module structure of Ω over S induced by the differential operator D, in order to make D an S-linear morphism wh...

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Detalles Bibliográficos
Autor principal: Molinuevo, Ariel
Publicado: 2016
Materias:
Differential operators
Exterior algebra
Modules
Order one
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01384821_v57_n4_p771_Molinuevo
http://hdl.handle.net/20.500.12110/paper_01384821_v57_n4_p771_Molinuevo
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling paper:paper_01384821_v57_n4_p771_Molinuevo2023-06-08T15:10:57Z Deformations of the exterior algebra of differential forms Molinuevo, Ariel Differential operators Exterior algebra Modules Order one Let D: Ω → Ω be a differential operator defined in the exterior algebra Ω of differential forms over the polynomial ring S in n variables. In this work we give conditions for deforming the module structure of Ω over S induced by the differential operator D, in order to make D an S-linear morphism while leaving the C-vector space structure of Ω unchanged. One can then apply the usual algebraic tools to study differential operators: finding generators of the kernel and image, computing a Hilbert polynomial of these modules, etc. Taking differential operators arising from a distinguished family of derivations, we are able to classify which of them allow such deformations on Ω. Finally we give examples of differential operators and the deformations that they induce. © 2016, The Managing Editors. Fil:Molinuevo, A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2016 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01384821_v57_n4_p771_Molinuevo http://hdl.handle.net/20.500.12110/paper_01384821_v57_n4_p771_Molinuevo
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Differential operators
Exterior algebra
Modules
Order one
spellingShingle Differential operators
Exterior algebra
Modules
Order one
Molinuevo, Ariel
Deformations of the exterior algebra of differential forms
topic_facet Differential operators
Exterior algebra
Modules
Order one
description Let D: Ω → Ω be a differential operator defined in the exterior algebra Ω of differential forms over the polynomial ring S in n variables. In this work we give conditions for deforming the module structure of Ω over S induced by the differential operator D, in order to make D an S-linear morphism while leaving the C-vector space structure of Ω unchanged. One can then apply the usual algebraic tools to study differential operators: finding generators of the kernel and image, computing a Hilbert polynomial of these modules, etc. Taking differential operators arising from a distinguished family of derivations, we are able to classify which of them allow such deformations on Ω. Finally we give examples of differential operators and the deformations that they induce. © 2016, The Managing Editors.
author Molinuevo, Ariel
author_facet Molinuevo, Ariel
author_sort Molinuevo, Ariel
title Deformations of the exterior algebra of differential forms
title_short Deformations of the exterior algebra of differential forms
title_full Deformations of the exterior algebra of differential forms
title_fullStr Deformations of the exterior algebra of differential forms
title_full_unstemmed Deformations of the exterior algebra of differential forms
title_sort deformations of the exterior algebra of differential forms
publishDate 2016
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01384821_v57_n4_p771_Molinuevo
http://hdl.handle.net/20.500.12110/paper_01384821_v57_n4_p771_Molinuevo
work_keys_str_mv AT molinuevoariel deformationsoftheexterioralgebraofdifferentialforms
_version_ 1768544173045055488

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