Weak amenability of group algebras of connected complex semisimple Lie groups
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- by B. E. Johnson PDF
- Proc. Amer. Math. Soc. 111 (1991), 177-185 Request permission
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
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Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 111 (1991), 177-185
- MSC: Primary 43A20; Secondary 22D15, 22E46
- DOI: https://doi.org/10.1090/S0002-9939-1991-1023344-6
- MathSciNet review: 1023344