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Mathematics > Operator Algebras
Title: A categorical study on the generalized type semigroup
(Submitted on 22 Jul 2021 (v1), last revised 22 Jun 2022 (this version, v2))
Abstract: In this short note, we show that the generalized type semigroup $\CW(X, \Gamma)$ introduced by the author in \cite{M3} belongs to the category \textnormal{W}. In particular, we demonstrate that $\CW(X, \Gamma)$ satisfies axioms (W1)-(W4) and (W6). When $X$ is zero-dimensional, we also establish (W5) for the semigroup. This supports the analogy between the generalized type semigroup and pre-completed Cuntz semigroup $W(\cdot)$ for $C^*$-algebras.
Submission history
From: Xin Ma [view email][v1] Thu, 22 Jul 2021 17:12:19 GMT (9kb)
[v2] Wed, 22 Jun 2022 19:11:41 GMT (11kb)
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