Journal of Lie Theory

no. 1
The Problem of Zero Divisors in Convolution Algebras of Supersolvable Lie Groups
Journal of Lie Theory, Volume 23 (2013) no. 1, pp. 119-125
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.
DOI: 10.5802/jolt.718
Classification: 22A25, 43A10
Keywords: Convolution, convolution algebra, zero divisor, compactly supported measure 
@article{JOLT_2013_23_1_a5,
     author = {L. Garncarek},
     title = {The {Problem} of {Zero} {Divisors} in {Convolution} {Algebras} of {Supersolvable} {Lie} {Groups}},
     journal = {Journal of Lie Theory},
     pages = {119--125},
     year = {2013},
     volume = {23},
     number = {1},
     doi = {10.5802/jolt.718},
     zbl = {1271.22004},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.718/}
}
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L. Garncarek. The Problem of Zero Divisors in Convolution Algebras of Supersolvable Lie Groups. Journal of Lie Theory, Volume 23 (2013) no. 1, pp. 119-125. doi: 10.5802/jolt.718

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