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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Weak amenability of group algebras of connected complex semisimple Lie groups


Author: B. E. Johnson
Journal: Proc. Amer. Math. Soc. 111 (1991), 177-185
MSC: Primary 43A20; Secondary 22D15, 22E46
MathSciNet review: 1023344
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Abstract: We consider the problem of whether every continuous derivation from a group algebra $ {L^1}(G)$ into its dual $ {L^\infty }(G)$ (where the $ {L^1}(G)$ actions on $ {L^\infty }(G)$ are the adjoint of multiplication in $ {L^1}(G)$ is inner, that is, of the form $ D(a) = aF - Fa$ for some $ F \in {L^\infty }(G)$. This had previously been established to hold for discrete and amenable groups and is now established for $ G = {\text{Gl(}}n,{\mathbf{C}})$ and for all connected semisimple complex Lie groups.


References [Enhancements On Off] (What's this?)

  • [1] Edwin Hewitt and Kenneth A. Ross, Abstract harmonic analysis. Vol. I, 2nd ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 115, Springer-Verlag, Berlin-New York, 1979. Structure of topological groups, integration theory, group representations. MR 551496 (81k:43001)
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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1023344-6
PII: S 0002-9939(1991)1023344-6
Article copyright: © Copyright 1991 American Mathematical Society