A categorical study on the generalized type semigroup
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- by Xin Ma;
- Proc. Amer. Math. Soc. 151 (2023), 1561-1568
- DOI: https://doi.org/10.1090/proc/16193
- Published electronically: January 30, 2023
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Abstract:
In this short note, we show that the generalized type semigroup $\mathcal {W}(X, \Gamma )$ introduced by Ma [Ergodic Theory Dynam. Systems 41 (2021), pp. 2148–2165] belongs to the category W introduced by Antoine, Perera and Theil [Mem. Amer. Math. Soc. 251 (2018), vii+191]. In particular, we demonstrate that $\mathcal {W}(X, \Gamma )$ 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.References
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Bibliographic Information
- Xin Ma
- Affiliation: Department of Mathematics, University of Memphis, Memphis, Tennessee, 38152
- MR Author ID: 1256218
- Email: xma1@memphis.edu
- Received by editor(s): July 29, 2021
- Received by editor(s) in revised form: June 8, 2022, and June 19, 2022
- Published electronically: January 30, 2023
- Communicated by: Adrian Ioana
- © Copyright 2023 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 151 (2023), 1561-1568
- MSC (2020): Primary 46L35, 37B05
- DOI: https://doi.org/10.1090/proc/16193
- MathSciNet review: 4550351