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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todo:paper_00224049_v222_n8_p2006_Beltran2023-10-03T14:32:45Z Central extensions of the algebra of formal pseudo-differential symbols via Hochschild (co)homology and quadratic symplectic Lie algebras Beltran, J. Farinati, M. Reyes, E.G. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00224049_v222_n8_p2006_Beltran |
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Universidad de Buenos Aires |
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I-28 |
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R-134 |
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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. |
| format |
JOUR |
| author |
Beltran, J. Farinati, M. Reyes, E.G. |
| spellingShingle |
Beltran, J. Farinati, M. Reyes, E.G. Central extensions of the algebra of formal pseudo-differential symbols via Hochschild (co)homology and quadratic symplectic Lie algebras |
| author_facet |
Beltran, J. Farinati, M. Reyes, E.G. |
| author_sort |
Beltran, J. |
| title |
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 |
| url |
http://hdl.handle.net/20.500.12110/paper_00224049_v222_n8_p2006_Beltran |
| work_keys_str_mv |
AT beltranj centralextensionsofthealgebraofformalpseudodifferentialsymbolsviahochschildcohomologyandquadraticsymplecticliealgebras AT farinatim centralextensionsofthealgebraofformalpseudodifferentialsymbolsviahochschildcohomologyandquadraticsymplecticliealgebras AT reyeseg centralextensionsofthealgebraofformalpseudodifferentialsymbolsviahochschildcohomologyandquadraticsymplecticliealgebras |
| _version_ |
1807314647137648640 |