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<p>For a class of wreath-like product groups with property (T), we describe explicitly all the embeddings between their von Neumann algebras. This allows us to provide a continuum of ICC groups with property (T) whose von Neumann algebras are pairwise non (stably) embeddable. We also give a construction of groups in this class only having inner injective homomorphisms. As an application, we obtain examples of group von Neumann algebras which admit only inner endomorphisms.</p>

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Wreath-Like Products of Groups and their von Neumann Algebras III: Embeddings

  • 期刊论文

  • 发表日期：

    2026年1月15日

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  • Ionuţ Chifan,
  • Adrian Ioana,
  • Denis Osin,
  • Bin Sun

摘要

For a class of wreath-like product groups with property (T), we describe explicitly all the embeddings between their von Neumann algebras. This allows us to provide a continuum of ICC groups with property (T) whose von Neumann algebras are pairwise non (stably) embeddable. We also give a construction of groups in this class only having inner injective homomorphisms. As an application, we obtain examples of group von Neumann algebras which admit only inner endomorphisms.