Deformations of the exterior algebra of differential forms

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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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Autor principal: Molinuevo, A.
Formato: JOUR
Materias:
Differential operators
Exterior algebra
Modules
Order one
Acceso en línea: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 todo:paper_01384821_v57_n4_p771_Molinuevo2023-10-03T14:58:09Z Deformations of the exterior algebra of differential forms Molinuevo, A. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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, A.
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.
format JOUR
author Molinuevo, A.
author_facet Molinuevo, A.
author_sort Molinuevo, A.
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
url http://hdl.handle.net/20.500.12110/paper_01384821_v57_n4_p771_Molinuevo
work_keys_str_mv AT molinuevoa deformationsoftheexterioralgebraofdifferentialforms
_version_ 1807315802995556352

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