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

In: Algebra and Operator Theory

Author

Listed:
  • J. Alev

    (Université de Reims, Département de Mathématiques)

  • T. Lambre

    (Université de Paris Sud, Département de Mathématiques)

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.

Suggested Citation

  • J. Alev & T. Lambre, 1998. "Comparaison de L’Homologie de Hochschild et de L’Homologie de Poisson Pour Une Deformation des Surfaces de Klein," Springer Books, in: Yusupdjan Khakimdjanov & Michel Goze & Shavkat A. Ayupov (ed.), Algebra and Operator Theory, pages 25-38, Springer.
    • Handle: RePEc:spr:sprchp:978-94-011-5072-9_3
    DOI: 10.1007/978-94-011-5072-9_3
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