Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Hochschild homology and cohomology of $\ell^1(\mathbb Z_+^k)$
AU - Choi, Yemon
PY - 2010
Y1 - 2010
N2 - Building on the recent determination of the simplicial cohomology groups of the convolution algebra ℓ1(ℤk+) [F. Gourdeau, Z. A. Lykova and M. C. White, A Künneth formula in topological homology and its applications to the simplicial cohomology of ℓ1(ℤk+), Studia Math. 166 (2005), 29–54], we investigate what can be said for the cohomology of this algebra with more general symmetric coefficients. Our approach leads us to a discussion of the Harrison homology and cohomology in the context of Banach algebras and a development of some of its basic features. As an application of our techniques, we reprove some known results on second-degree cohomology.
AB - Building on the recent determination of the simplicial cohomology groups of the convolution algebra ℓ1(ℤk+) [F. Gourdeau, Z. A. Lykova and M. C. White, A Künneth formula in topological homology and its applications to the simplicial cohomology of ℓ1(ℤk+), Studia Math. 166 (2005), 29–54], we investigate what can be said for the cohomology of this algebra with more general symmetric coefficients. Our approach leads us to a discussion of the Harrison homology and cohomology in the context of Banach algebras and a development of some of its basic features. As an application of our techniques, we reprove some known results on second-degree cohomology.
U2 - 10.1093/qmath/han027
DO - 10.1093/qmath/han027
M3 - Journal article
VL - 61
SP - 1
EP - 28
JO - The Quarterly Journal of Mathematics
JF - The Quarterly Journal of Mathematics
SN - 0033-5606
IS - 1
ER -