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 into its dual (where the actions on are the adjoint of multiplication in is inner, that is, of the form for some . This had previously been established to hold for discrete and amenable groups and is now established for and for all connected semisimple complex Lie groups.
-  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
-  Barry Edward Johnson, Cohomology in Banach algebras, American Mathematical Society, Providence, R.I., 1972. Memoirs of the American Mathematical Society, No. 127. MR 0374934
-  -, Derivations from into and , Lecture Notes in Math., vol. 1359, Springer, Berlin and New York, 1988, pp. 191-198.
- E. Hewitt and K.A. Ross, Abstract harmonic analysis, vol. II, Springer-Verlag, Berlin, 1970. MR 551496 (81k:43001)
- B.E. Johnson, Cohomology in Banach algebras, Mem. Amer. Math. Soc. 127 (1972). MR 0374934 (51:11130)
- -, Derivations from into and , Lecture Notes in Math., vol. 1359, Springer, Berlin and New York, 1988, pp. 191-198.