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Hochschild homology and cohomology of $\ell^1(\mathbb Z_+^k)$

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Hochschild homology and cohomology of $\ell^1(\mathbb Z_+^k)$. / Choi, Yemon.
In: The Quarterly Journal of Mathematics, Vol. 61, No. 1, 2010, p. 1-28.

Research output: Contribution to Journal/MagazineJournal articlepeer-review

Harvard

Choi, Y 2010, 'Hochschild homology and cohomology of $\ell^1(\mathbb Z_+^k)$', The Quarterly Journal of Mathematics, vol. 61, no. 1, pp. 1-28. https://doi.org/10.1093/qmath/han027

APA

Vancouver

Choi Y. Hochschild homology and cohomology of $\ell^1(\mathbb Z_+^k)$. The Quarterly Journal of Mathematics. 2010;61(1):1-28. doi: 10.1093/qmath/han027

Author

Choi, Yemon. / Hochschild homology and cohomology of $\ell^1(\mathbb Z_+^k)$. In: The Quarterly Journal of Mathematics. 2010 ; Vol. 61, No. 1. pp. 1-28.

Bibtex

@article{b266da82d518425a9527b9ec9066b280,
title = "Hochschild homology and cohomology of $\ell^1(\mathbb Z_+^k)$",
abstract = "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 K{\"u}nneth 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. ",
author = "Yemon Choi",
year = "2010",
doi = "10.1093/qmath/han027",
language = "Undefined/Unknown",
volume = "61",
pages = "1--28",
journal = "The Quarterly Journal of Mathematics",
issn = "0033-5606",
publisher = "Oxford University Press",
number = "1",

}

RIS

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 -