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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
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  • [3] -, Derivations from $ {L^1}(G)$ into $ {L^1}(G)$ and $ {L^\infty }(G)$, Lecture Notes in Math., vol. 1359, Springer, Berlin and New York, 1988, pp. 191-198.

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Article copyright: © Copyright 1991 American Mathematical Society