hal-00129712, version 1

Hochschild and cyclic homology of the quantum multiparametric torus.

Marc Wambst ¹

(1994-10-01)

• 1:  Institut de Recherche Mathématique Avancée (IRMA)
• http://www-irma.u-strasbg.fr/
  CNRS : UMR7501 – Université Louis Pasteur - Strasbourg I 7 rue René-Descartes, 67084 Strasbourg Cedex, France France

Bibliographic reference

• Type of document: Documents without publication reference (Preprint)
• Subject: Mathematics/Rings and Algebras
• Title: Hochschild and cyclic homology of the quantum multiparametric torus.
• Abstract: The quantum multiparametric torus is the algebra generated over a field $k$ by the $2N$ variables $x_1,\ldots,x_N$ and $x_1^{-1},\ldots,x_N^{-1}$ and the relations $ x_ix_i^{-1}=1=x_i^{-1} x_i$ and $x_ix_j=q_{ij}x_jx_i$ for every $1\le i,j\le N$ and where $\{q_{ij}\}_{1\le i,j\le N}$ is a family of non-zero scalars of $k$ satisfying the relations $q_{ii}=1$ and $q_{ij}q_{ji}=1$ for every $1\le i,j,\le N$. We explicitly compute its Hochschild homology groups, using previously constructed ``quantum Koszul complexes''. We deduce the corresponding cyclic homology groups.
• Fulltext language: English
• Production date: 1994-10-01
• Keyword(s): "Quantum algebras – quantum torus – Hochschild homology – cyclic homology – Koszul complexes"
• Classification: 17B37, 18G50, 18G60

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• http://hal.archives-ouvertes.fr/hal-00129712
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• From: Véronique Bertrand <>
• Submitted on: Thursday, 8 February 2007 15:00:35
• Updated on: Thursday, 8 February 2007 17:07:28