Periodic cyclic homology of Iwahori-Hecke algebras
| dc.creator | Baum, Paul | |
| dc.creator | Nistor, Victor | |
| dc.date | 2002-01-21 | |
| dc.date.accessioned | 2026-07-07T04:46:01Z | |
| dc.date.available | 2026-07-07T04:46:01Z | |
| dc.description | We determine the periodic cyclic homology of the Iwahori-Hecke algebras $\Hecke_q$, for $q \in \CC^*$ not a ``proper root of unity.'' (In this paper, by a {\em proper root of unity} we shall mean a root of unity other than 1.) Our method is based on a general result on periodic cyclic homology, which states that a ``weakly spectrum preserving'' morphism of finite type algebras induces an isomorphism in periodic cyclic homology. The concept of a weakly spectrum preserving morphism is defined in this paper, and most of our work is devoted to understanding this class of morphisms. Results of Kazhdan--Lusztig and Lusztig show that, for the indicated values of $q$, there exists a weakly spectrum preserving morphism $ϕ_q : \Hecke_q \to J$, to a fixed finite type algebra $J$. This proves that $ϕ_q$ induces an isomorphism in periodic cyclic homology and, in particular, that all algebras $\Hecke_q$ have the same periodic cyclic homology, for the indicated values of $q$. The periodic cyclic homology groups of the algebra $\Hecke_1$ can then be determined directly, using results of Karoubi and Burghelea, because it is the group algebra of an extended affine Weyl group. | |
| dc.description | 24 pages, LaTeX | |
| dc.identifier | https://arxiv.org/abs/math/0201201 | |
| dc.identifier | http://arxiv.org/abs/math/0201201 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63169 | |
| dc.subject | K-Theory and Homology | |
| dc.subject | Operator Algebras | |
| dc.subject | Representation Theory | |
| dc.title | Periodic cyclic homology of Iwahori-Hecke algebras | |
| dc.type | text |