New examples of Property (T) factors with trivial fundamental group and unique prime factorization

2020/11/09 by Sayan Das, Das, Sayan
Mathematics · #FOS: Mathematics #Operator Algebras (math.OA) #math.OA

paper · pdf · doi:10.48550/arxiv.2011.04487

Comments welcome

arxiv created 2020/11/09 · arxiv updated 2020/11/10

Abstract

In this paper we provide new examples of property (T) group factors with trivial fundamental group thereby providing more evidence towards Popa's conjecture on triviality of fundamental groups for property (T) group factors (page 9 \citePo13; see also Problem 2, page 551 in Connes' book \citeCo94). Our groups arise as direct product of groups either in Class \mathscr S or Class \mathscr V, as introduced in \citeCDHK20. We establish a unique prime factorization result for these product groups, thereby providing more evidence towards Popa's conjecture on prime decomposition of property (T) factors (page 9 \citePo13).

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