English

The problem of zero divisors in convolution algebras of supersolvable Lie groups

Group Theory 2013-04-11 v2 Functional Analysis Rings and Algebras

Abstract

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

Cite

@article{arxiv.1110.3692,
  title  = {The problem of zero divisors in convolution algebras of supersolvable Lie groups},
  author = {Łukasz Garncarek},
  journal= {arXiv preprint arXiv:1110.3692},
  year   = {2013}
}

Comments

6 pages; Current revision: extended the Introduction; added more references; partially rewritten Section 3, hopefully making it more clear