The cyclic homology of the group rings

Burghelea, Dan

doi:10.1007/bf02567420

Cited by 143 publications

(95 citation statements)

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“…This isomorphism can be made natural by using a generalization of the Shalika germs. The isomorphism (1.3) is in the spirit of the results of Karoubi [13] and Burghelea [8]. See also [10].…”

Section: W G (A) := N G (A)/c G (A) and Z(a) := A ∩ C G (A)mentioning

confidence: 77%

Higher orbital integrals, Shalika germs, and the Hochschild homology of Hecke algebras

Nistor

2001

International Journal of Mathematics and Mathematical Sciences

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Abstract. We give a detailed calculation of the Hochschild and cyclic homology of the algebra Ꮿ ∞ c (G) of locally constant, compactly supported functions on a reductive p-adic group G. We use these calculations to extend to arbitrary elements the definition of the higher orbital integrals introduced by Blanc and Brylinski (1992) for regular semi-simple elements. Then we extend to higher orbital integrals some results of Shalika (1972). We also investigate the effect of the "induction morphism" on Hochschild homology.2000 Mathematics Subject Classification. 19D55, 46L80, 16E40.

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Section: W G (A) := N G (A)/c G (A) and Z(a) := A ∩ C G (A)mentioning

confidence: 77%

Higher orbital integrals, Shalika germs, and the Hochschild homology of Hecke algebras

Nistor

2001

International Journal of Mathematics and Mathematical Sciences

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“…As in the case of compact groups, one obtains a very good description of Hochschild homology. First one has a decomposition of HHp(.^) into direct summands HHp(j^)^, indexed by conjugacy classes CO in G. For the case X is a point, this is due to Burghelea [14]. If CO is the class of y, HHp(jaQ(r is the abutment of a spectral sequence E^ = H,(G,,H/C?(X),(C?…”

Section: Definition -^ Is the Subsheaf Of C°°-functions On X/g Consimentioning

confidence: 99%

Cyclic homology and equivariant theories

Brylinski¹

1987

Annales De L’institut Fourier

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“…The cyclic homology of the group algebra A = R (devoid of any topology) has been studied notably by D. Burghelea [29]. For an example with a locally convex completion of A, smaller than 1 ( ) and closer to the spirit of [37], see R. Ji [87].…”

Section: Cohomology Of Group Algebrasmentioning

confidence: 99%