Cyclic homology of strong smash product algebras

Jiao Zhang; Naihong Hu

doi:10.1515/CRELLE.2011.098

Cyclic homology of strong smash product algebras

Jiao Zhang^*
, Naihong Hu

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

For any strong smash product algebra A# _RB of two algebras A and B with a bijective morphism R mapping from B ⊗ A to A × B, we construct a cylindrical module A B whose diagonal cyclic module Δ _• (A B) is graphically proven to be isomorphic to C _• (A# _RB) the cyclic module of the algebra. A spectral sequence is established to converge to the cyclic homology of A# _RB. Examples are provided to show how our results work. Particularly, the cyclic homology of the Pareigis' Hopf algebra is obtained in the way.

Original language	English
Pages (from-to)	177-207
Number of pages	31
Journal	Journal fur die Reine und Angewandte Mathematik
Issue number	663
DOIs	https://doi.org/10.1515/CRELLE.2011.098
State	Published - Feb 2012

Access to Document

10.1515/CRELLE.2011.098

Cite this

@article{a74e9f668d9640928a9bca8ded8a3c1a,

title = "Cyclic homology of strong smash product algebras",

abstract = "For any strong smash product algebra A\# RB of two algebras A and B with a bijective morphism R mapping from B ⊗ A to A × B, we construct a cylindrical module A B whose diagonal cyclic module Δ • (A B) is graphically proven to be isomorphic to C • (A\# RB) the cyclic module of the algebra. A spectral sequence is established to converge to the cyclic homology of A\# RB. Examples are provided to show how our results work. Particularly, the cyclic homology of the Pareigis' Hopf algebra is obtained in the way.",

author = "Jiao Zhang and Naihong Hu",

year = "2012",

month = feb,

doi = "10.1515/CRELLE.2011.098",

language = "英语",

pages = "177--207",

journal = "Journal fur die Reine und Angewandte Mathematik",

issn = "0075-4102",

publisher = "Walter de Gruyter GmbH",

number = "663",

}

TY - JOUR

T1 - Cyclic homology of strong smash product algebras

AU - Zhang, Jiao

AU - Hu, Naihong

PY - 2012/2

Y1 - 2012/2

N2 - For any strong smash product algebra A# RB of two algebras A and B with a bijective morphism R mapping from B ⊗ A to A × B, we construct a cylindrical module A B whose diagonal cyclic module Δ • (A B) is graphically proven to be isomorphic to C • (A# RB) the cyclic module of the algebra. A spectral sequence is established to converge to the cyclic homology of A# RB. Examples are provided to show how our results work. Particularly, the cyclic homology of the Pareigis' Hopf algebra is obtained in the way.

AB - For any strong smash product algebra A# RB of two algebras A and B with a bijective morphism R mapping from B ⊗ A to A × B, we construct a cylindrical module A B whose diagonal cyclic module Δ • (A B) is graphically proven to be isomorphic to C • (A# RB) the cyclic module of the algebra. A spectral sequence is established to converge to the cyclic homology of A# RB. Examples are provided to show how our results work. Particularly, the cyclic homology of the Pareigis' Hopf algebra is obtained in the way.

UR - https://www.scopus.com/pages/publications/84859852858

U2 - 10.1515/CRELLE.2011.098

DO - 10.1515/CRELLE.2011.098

M3 - 文章

AN - SCOPUS:84859852858

SN - 0075-4102

SP - 177

EP - 207

JO - Journal fur die Reine und Angewandte Mathematik

JF - Journal fur die Reine und Angewandte Mathematik

IS - 663

ER -

Cyclic homology of strong smash product algebras

Abstract

Access to Document

Other files and links

Fingerprint

Cite this