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Higher Dimensional Cohomology of Weighted Sequence Algebras

Part of: Abstract harmonic analysis Methods of category theory in functional analysis

Published online by Cambridge University Press:  09 April 2009

A. Pourabbas
A. Pourabbas
Affiliation:
Faculty of Mathematics and Computer Science Amir Kabir University424 Hafez Avenue Tehran 15914Iran e-mail: arpabbas@au.ac.ir
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Abstract

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It is well known that c0(Z) is amenable and so its global dimension is zero. In this paper we will investigate the cyclic and Hochschild cohomology of Banach algebra c0 (Z, ω-1) and its unitisation with coefficients in its dual space, where ω is a weight on Z which satisfies inf {ω(i)} = 0.Moreover we show that the weak homological bi-dimension of c0 (Z, ω-1) is infinity.

MSC classification

Secondary: 46M20: Methods of algebraic topology (cohomology, sheaf and bundle theory, etc.) 43A15: $L^p$-spaces and other function spaces on groups, semigroups, etc.
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 75 , Issue 1 , August 2003 , pp. 57 - 68
Copyright
Copyright © Australian Mathematical Society 2003

References

[1]Bade, W. G., Curtis, P. C. Jr, and Dales, H. G., ‘Amenability and weak amenability for Beurling and Lipschitz algebras’, Proc. London Math. Soc. 55 (1987), 359–377.CrossRefGoogle Scholar
[2]Dales, H. G. and Duncan, J., ‘Second order cohomology groups of some semigroup algebras’, in: Banach Algebra'97 (Blaubeuren) (Walter de Gruyter, Berlin, 1998) pp. 101–117.CrossRefGoogle Scholar
[3]Dales, H. G., Ghahramani, F. and Grønbæk, N., ‘Derivation into iterated duals of Banach algebras’, Studia Math. 128 (1998), 19–54.Google Scholar
[4]Gourdeau, F. and White, M. C., ‘Vanishing of the third simplicial cohomology group of l 1(Z +)’, Trans. Amer. Math. Soc. 353 (2001), 2003–2017.CrossRefGoogle Scholar
[5]Grønbæk, N., ‘Weak and cyclic amenability for non-commutative Banach algebras’, Proc. Edinburgh Math. Soc. 35 (1992), 315–328.CrossRefGoogle Scholar
[6]Helemskii, A. Ya., The homology of Banach and topological algebras (Kluwer Academic Publishers, Dordrecht, 1986).Google Scholar
[7]Helemskii, A. Ya., Banach and locally convex algebras (Oxford University Press, Oxford, 1993).CrossRefGoogle Scholar
[8]Johnson, B. E., Cohomology in Banach algebras, Mem. Amer. Math. Soc. 127 (Amer. Math. Soc. Providence, 1972).CrossRefGoogle Scholar
[9]Johnson, B. E., Derivations from L1(G) into L1(G) and L∞(G), Lecture Notes in Math. 1359 (Springer, Berlin, 1988) pp. 191–198.Google Scholar
[10]Johnson, B. E., ‘Alternating cohomology’, Preprint.Google Scholar
[11]Johnsona, B. E., Kadison, R. V. and Ringrose, J. R., ‘Cohomology of operator algebra III. Reduction to normal cohomology’, Bull. Soc. Math. France 100 (1972), 73–96.CrossRefGoogle Scholar
[12]Lykova, Z. A., ‘Relative cohomology of Banach algebras’, J. Operator Theory 41 (1999), 23–53.Google Scholar
[13]Selivanov, Yu. V., ‘Weak homological bi-dimension and its values in the class of biflat Banach algebras’, Extracta Math. 11 (1996), 348–365.Google Scholar
[14]Sinclair, A. M. and Smith, R. R., Hochschild cohomology of von Neumann algebras, London Math. Soc. Lecture Note Ser. 204 (Cambridge Univ. Press, Cambridge, 1995) pp. 196.CrossRefGoogle Scholar