Central Functions in Group Algebras

  title={Central Functions in Group Algebras},
  author={RICHARD D. MOSAK and R. D. MOSAK},
  • Published 2010
In this paper we show that for a locally compact group G, the group algebra -Li(G) has nontrivial center if and only if G possesses a compact neighborhood of 1, invariant under inner automorphisms. Moreover, G has a basis of such neighborhoods at 1 if and only if Z-i(G) has an approximate identity consisting of functions in the center of L\. This constitutes part of a program of finding conditions on the group algebra which characterize groups satisfying various compactness conditions (see e.g… CONTINUE READING


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