Boundary Quotient -algebras of Products of Odometers
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Bibliographic record
Abstract
Abstract In this paper, we study the boundary quotient $\text{C}^{\ast }$ -algebras associated with products of odometers. One of our main results shows that the boundary quotient $\text{C}^{\ast }$ -algebra of the standard product of $k$ odometers over $n_{i}$ -letter alphabets $(1\leqslant i\leqslant k)$ is always nuclear, and that it is a UCT Kirchberg algebra if and only if $\{\ln n_{i}:1\leqslant i\leqslant k\}$ is rationally independent, if and only if the associated single-vertex $k$ -graph $\text{C}^{\ast }$ -algebra is simple. To achieve this, one of our main steps is to construct a topological $k$ -graph such that its associated Cuntz–Pimsner $\text{C}^{\ast }$ -algebra is isomorphic to the boundary quotient $\text{C}^{\ast }$ -algebra. Some relations between the boundary quotient $\text{C}^{\ast }$ -algebra and the $\text{C}^{\ast }$ -algebra $\text{Q}_{\mathbb{N}}$ introduced by Cuntz are also investigated.
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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.008 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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