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Journal of Lie Theory 31 (2021), No. 4, 969--974
Copyright Heldermann Verlag 2021

Applications of Lie Theory to Daws' Conjecture on Ultrapowers of Locally Compact Group Algebras

Maedeh Soroushmehr
School of Mathematics, Institute for Research in Fundamental Science, Tehran, Iran

Focusing on the fact that a locally compact group G may be approximated by Lie groups, we show that for a given locally compact group G, L1(G) is ultra-amenable if and only if G is finite. Thus we answer a question raised by M. Daws in 2009.

Keywords: Locally compact group, Lie group, semisimple Lie group, ultrapower, group algebra.

MSC: 46B08; 22E46, 22E20, 46H05, 22D15.

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