Central extensions of the algebra of formal pseudo-differential symbols via Hochschild (co)homology and quadratic symplectic Lie algebras

We describe the space of central extensions of the associative algebra Ψn of formal pseudo-differential symbols in n≥1 independent variables using Hochschild (co)homology groups: we prove that the first Hochschild (co)homology group HH1(Ψn) is 2n-dimensional and we use this fact to calculate the fir...

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Publicado: 2018
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00224049_v222_n8_p2006_Beltran
http://hdl.handle.net/20.500.12110/paper_00224049_v222_n8_p2006_Beltran
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00224049_v222_n8_p2006_Beltran
record_format dspace
spelling paper:paper_00224049_v222_n8_p2006_Beltran2023-06-08T14:50:44Z Central extensions of the algebra of formal pseudo-differential symbols via Hochschild (co)homology and quadratic symplectic Lie algebras We describe the space of central extensions of the associative algebra Ψn of formal pseudo-differential symbols in n≥1 independent variables using Hochschild (co)homology groups: we prove that the first Hochschild (co)homology group HH1(Ψn) is 2n-dimensional and we use this fact to calculate the first Lie (co)homology group HLie 1(Ψn) of Ψn equipped with the Lie bracket induced by its associative algebra structure. As an application, we use our calculations to provide examples of infinite-dimensional quadratic symplectic Lie algebras. © 2017 Elsevier B.V. 2018 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00224049_v222_n8_p2006_Beltran http://hdl.handle.net/20.500.12110/paper_00224049_v222_n8_p2006_Beltran
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description We describe the space of central extensions of the associative algebra Ψn of formal pseudo-differential symbols in n≥1 independent variables using Hochschild (co)homology groups: we prove that the first Hochschild (co)homology group HH1(Ψn) is 2n-dimensional and we use this fact to calculate the first Lie (co)homology group HLie 1(Ψn) of Ψn equipped with the Lie bracket induced by its associative algebra structure. As an application, we use our calculations to provide examples of infinite-dimensional quadratic symplectic Lie algebras. © 2017 Elsevier B.V.
title Central extensions of the algebra of formal pseudo-differential symbols via Hochschild (co)homology and quadratic symplectic Lie algebras
spellingShingle Central extensions of the algebra of formal pseudo-differential symbols via Hochschild (co)homology and quadratic symplectic Lie algebras
title_short Central extensions of the algebra of formal pseudo-differential symbols via Hochschild (co)homology and quadratic symplectic Lie algebras
title_full Central extensions of the algebra of formal pseudo-differential symbols via Hochschild (co)homology and quadratic symplectic Lie algebras
title_fullStr Central extensions of the algebra of formal pseudo-differential symbols via Hochschild (co)homology and quadratic symplectic Lie algebras
title_full_unstemmed Central extensions of the algebra of formal pseudo-differential symbols via Hochschild (co)homology and quadratic symplectic Lie algebras
title_sort central extensions of the algebra of formal pseudo-differential symbols via hochschild (co)homology and quadratic symplectic lie algebras
publishDate 2018
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00224049_v222_n8_p2006_Beltran
http://hdl.handle.net/20.500.12110/paper_00224049_v222_n8_p2006_Beltran
_version_ 1768542492870836224

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