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A relationship between HNN extensions and amalgamated free products in operator algebras

Yoshimichi Ueda
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Abstract

With a minor change made in the previous construction we observe that any reduced HNN extension is precisely a compressed algebra of a certain reduced amalgamated free product in both the von Neumann algebra and the $C^*$-algebra settings. It is also pointed out that the same fact holds true even for universal HNN extensions of C$^*$-algebras. We apply the observation to the questions of factoriality and type classification of HNN extensions of von Neumann algebras and also those of simplicity and $K$-theory of (reduced or universal) HNN extensions of $C^*$-algebras.

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Yoshimichi Ueda. 2008-04-02. A relationship between HNN extensions and amalgamated free products in operator algebras. https://arxiv.org/abs/math/0601706

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