Weak amenability of group algebras of connected complex semisimple Lie groups
B. E. Johnson
Proc. Amer. Math. Soc. 111 (1991), 177-185
Primary 43A20; Secondary 22D15, 22E46
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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.
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
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.
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