INVESTIGADORES
FARINATI Marco Andres
artículos
Título:
Central extensions of the algebra of formal pseudo-differential symbols via Hochschild (co)homology and quadratic symplectic Lie algebras
Autor/es:
J. BELTRAN, M. FARINATI, E. REYES
Revista:
JOURNAL OF PURE AND APPLIED ALGEBRA
Editorial:
ELSEVIER SCIENCE BV
Referencias:
Lugar: Amsterdam; Año: 2017
ISSN:
0022-4049
Resumen:
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 HH 1 (Ψ n ) is 2n-dimensional and we use this fact to calculate the first Lie (co)homology group H^1_{Lie) (Ψ ) of Ψ equipped with the Lie bracket induced by its associative algebra. As an application, we use our calculations to provide examples of infinite dimensional quadratic symplectic Lie algebras.
