
Journal of Lie Theory 23 (2013), No. 1, 119125 Copyright Heldermann Verlag 2013 The Problem of Zero Divisors in Convolution Algebras of Supersolvable Lie Groups Lukasz Garncarek Mathematical Institute, University of Wroclaw, pl. Grunwaldzki 2/4, 50384 Wroclaw, Poland Lukasz.Garncarek@math.uni.wroc.pl We prove a variant of the Titchmarsh convolution theorem for simply connected supersolvable Lie groups, namely we show that the convolution algebras of compactly supported continuous functions and compactly supported finite measures on such groups do not contain zero divisors. This can be also viewed as a topological version of the zero divisor conjecture of Kaplansky. Keywords: Convolution, convolution algebra, zero divisor, compactly supported measure. MSC: 22A25, 43A10 [ Fulltextpdf (219 KB)] for subscribers only. 