Hochschild and cyclic homology of the quantum multiparametric torus.
Wambst, Marc
HAL, hal-00129712 / Harvested from HAL
Text on HAL
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.
Publié le : 1994-10-01
Classification:  Quantum algebras,  Koszul complexes,  "Quantum algebras,  quantum torus,  Hochschild homology,  cyclic homology,  Koszul complexes",  17B37, 18G50, 18G60,  [MATH.MATH-RA]Mathematics [math]/Rings and Algebras [math.RA] 
@article{hal-00129712,
     author = {Wambst, Marc},
     title = {Hochschild and cyclic homology of the quantum multiparametric torus.},
     journal = {HAL},
     volume = {1994},
     number = {0},
     year = {1994},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00129712}
}

Wambst, Marc. Hochschild and cyclic homology of the quantum multiparametric torus.. HAL, Tome 1994 (1994) no. 0, . http://gdmltest.u-ga.fr/item/hal-00129712/