A note on the Cuntz algebra automorphisms
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912684235030528 |
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| author | Pan, Junyao |
| author_facet | Pan, Junyao |
| contents | Permutative automorphisms of the Cuntz algebras $\mathcal{O}_n$ are in bijection with the stable permutations of $[n]^k$. They are also the elements of the restricted Weyl group of $Aut(\mathcal{O}_n)$. In this note, we characterize a class of stable involutions of $[n]^2$. More precisely, we prove Conjecture 12.2 of Brenti and Conti [Adv. Math. 381 (2021), p. 60], and thus providing a new family (with $6$ degrees of freedom) of automorphisms of the Cuntz algebras $\mathcal{O}_n$ for any $n>1$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_20318 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on the Cuntz algebra automorphisms Pan, Junyao Group Theory Operator Algebras 05E16, 05A05, 05A15 Permutative automorphisms of the Cuntz algebras $\mathcal{O}_n$ are in bijection with the stable permutations of $[n]^k$. They are also the elements of the restricted Weyl group of $Aut(\mathcal{O}_n)$. In this note, we characterize a class of stable involutions of $[n]^2$. More precisely, we prove Conjecture 12.2 of Brenti and Conti [Adv. Math. 381 (2021), p. 60], and thus providing a new family (with $6$ degrees of freedom) of automorphisms of the Cuntz algebras $\mathcal{O}_n$ for any $n>1$. |
| title | A note on the Cuntz algebra automorphisms |
| topic | Group Theory Operator Algebras 05E16, 05A05, 05A15 |
| url | https://arxiv.org/abs/2412.20318 |