Marc Wambst

Hochschild and cyclic homology of the quantum multiparametric torus.

Pure Appl. Algebra 114  (1997),  no. 3,  321-329.

Abstract : The quantum multiparametric torus is the algebra generated over a field k by the 2N variables x₁,...,x_N and x₁^-1,...,x_N^-1 and the relations x_ix_i^-1=1=x_i^-1x_iand x_ix_j=q_ijx_jx_i  for every 0< i,j< N+1 and where (q_ij)_{0< i,j< N+1} is a family of non-zero scalars of k satisfying the relations  q_ii=1and q_ijq_ji=1 for every 0< i,j< N+1. We explicitly compute its Hochschild homology groups, using previously constructed ``quantum Koszul complexes''. We deduce the corresponding cyclic homology groups.

Mots-clé,  Keywords : Quantum algebras,  quantum torus,  Hochschild homology,  cyclic homology,  Koszul
complexes

Classifications : 17B37, 18G50, 18G60 
 

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(Décembre 2006)