Comparaison de L’Homologie de Hochschild et de L’Homologie de Poisson Pour Une Deformation des Surfaces de Klein

J. Alev () and T. Lambre
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J. Alev: Université de Reims, Département de Mathématiques
T. Lambre: Université de Paris Sud, Département de Mathématiques

A chapter in Algebra and Operator Theory, 1998, pp 25-38 from Springer

Abstract: Abstract Let P G be the quotient variety of the affine plane by the action of a finite group G ⊂ SL(2,ℂ); then P G inherits in a natural way a Poisson algebra structure. Let A 1 (ℂ) be the first Weyl algebra ℂ[p, q] with the relation pq-qp=1, on which G acts by automorphisms in such a way that the invariant algebra A 1 (ℂ) G is a deformation of P G . We prove that the trace group HH 0(A 1(ℂ) G ) is a deformation of the Poisson homology group HH 0(A 1(ℂ) G ). Moreover, these two groups are ℂ-vector spaces of finite dimension and dim (HH 0(A 1(ℂ) G )) = dim (H 0 Pois (P G )) = s(G) - 1, where s(G) denotes the number of irreducible representations of G.

Keywords: Weyl Algebra; Cyclic Homology; Affine Plane; Invariant Algebra; Trace Group (search for similar items in EconPapers)
Date: 1998
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-011-5072-9_3

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DOI: 10.1007/978-94-011-5072-9_3

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