Abstract We describe the space of central extensions of the associative algebra Ψ n of formal pseudo-differential symbols in n ≥ 1 independent variables using Hochschild (co)homology groups: we prove… Click to show full abstract
Abstract We describe the space of central extensions of the associative algebra Ψ n of formal pseudo-differential symbols in n ≥ 1 independent variables using Hochschild (co)homology groups: we prove that the first Hochschild (co)homology group H H 1 ( Ψ n ) is 2n-dimensional and we use this fact to calculate the first Lie (co)homology group H L i e 1 ( Ψ n ) of Ψ n 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.
Journal Title: Journal of Pure and Applied Algebra
Year Published: 2017
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