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Abstract:

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.

Registro:

Documento: Artículo
Título:Central extensions of the algebra of formal pseudo-differential symbols via Hochschild (co)homology and quadratic symplectic Lie algebras
Autor:Beltran, J.; Farinati, M.; Reyes, E.G.
Filiación:Centro de Investigación en Complejidad Social (CICS), Facultad de Gobierno, Universidad del Desarrollo, Santiago, Chile
I.M.A.S., Depto. de Matemática, Fac. Cs. Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pab. 1, Buenos Aires, Argentina
Departamento de Matemática y Ciencia de la Computación, Universidad de Santiago de Chile, Casilla 307 Correo 2, Santiago, Chile
Año:2018
Volumen:222
Número:8
Página de inicio:2006
Página de fin:2021
DOI: http://dx.doi.org/10.1016/j.jpaa.2017.08.017
Título revista:Journal of Pure and Applied Algebra
Título revista abreviado:J. Pure Appl. Algebra
ISSN:00224049
CODEN:JPAAA
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00224049_v222_n8_p2006_Beltran

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Citas:

---------- APA ----------
Beltran, J., Farinati, M. & Reyes, E.G. (2018) . Central extensions of the algebra of formal pseudo-differential symbols via Hochschild (co)homology and quadratic symplectic Lie algebras. Journal of Pure and Applied Algebra, 222(8), 2006-2021.
http://dx.doi.org/10.1016/j.jpaa.2017.08.017
---------- CHICAGO ----------
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" . Journal of Pure and Applied Algebra 222, no. 8 (2018) : 2006-2021.
http://dx.doi.org/10.1016/j.jpaa.2017.08.017
---------- MLA ----------
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" . Journal of Pure and Applied Algebra, vol. 222, no. 8, 2018, pp. 2006-2021.
http://dx.doi.org/10.1016/j.jpaa.2017.08.017
---------- VANCOUVER ----------
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. J. Pure Appl. Algebra. 2018;222(8):2006-2021.
http://dx.doi.org/10.1016/j.jpaa.2017.08.017