Zero divisors with small supports in group algebras of torsion-free groups over a field

2020/12/25 by Sourav Koner, Koner, Sourav, Rabindranath Chakraborty +1
Mathematics · #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2012.13524

openalex publication_date 2020/12/25 · openalex created_date 2021/01/05 · openalex updated_date 2026/07/28

Abstract

For any field \mathbbF and all torison-free group \mathbbG, we prove that if ab = 0 for some non-zero a, b ∈ \mathbbF[\mathbbG] such that |supp(a)| = 3 and a = 1 + α₁g₁ + α₂g₂, then g₁, g₂ satisfies certain relations in \mathbbG.

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