A Necessary Condition for Zero Divisors in Complex Group Algebra of Torsion-Free Groups

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Abdollahi Alireza; Soleimani Malekan Meisam

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Journal Paper

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Journal: Iranian Journal of Mathematical Sciences and Informatics Year:2024 | Volume:19 | Issue:2 Page(s): 189-194

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Title

A Necessary Condition for Zero Divisors in Complex Group Algebra of Torsion-Free Groups

Author(s)

Abdollahi Alireza | Soleimani Malekan Meisam | Issue Writer Certificate

Keywords

Hilbert space $ell^2(G)$

Complex group algebras

Zero divisor conjecture

Torsion-free groups

Abstract

It is proved that if $sum_{gin G} a_g g$ is a non-zero zero divisor element of the complex group algebra $mathbb{C}G$ of a torsion-free group G then $2sum_{gin G} |a_g|^2

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