Heat semigroups on quantum automorphism groups of finite dimensional C*-algebras
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915685114839040 |
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| author | Sato, Futaba |
| author_facet | Sato, Futaba |
| contents | In this paper, we investigate heat semigroups on a quantum automorphism group ${\rm Aut}^+(B)$ of a finite dimensional C*-algebra $B$ and its Plancherel trace. We show ultracontractivity, hypercontractivity, and the spectral gap inequality of the heat semigroups on ${\rm Aut}^+(B)$. Furthermore, we obtain the sharpness of the Sobolev embedding property and the Hausdorff-Young inequality of ${\rm Aut}^+(B)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_03448 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Heat semigroups on quantum automorphism groups of finite dimensional C*-algebras Sato, Futaba Quantum Algebra Mathematical Physics Functional Analysis Operator Algebras In this paper, we investigate heat semigroups on a quantum automorphism group ${\rm Aut}^+(B)$ of a finite dimensional C*-algebra $B$ and its Plancherel trace. We show ultracontractivity, hypercontractivity, and the spectral gap inequality of the heat semigroups on ${\rm Aut}^+(B)$. Furthermore, we obtain the sharpness of the Sobolev embedding property and the Hausdorff-Young inequality of ${\rm Aut}^+(B)$. |
| title | Heat semigroups on quantum automorphism groups of finite dimensional C*-algebras |
| topic | Quantum Algebra Mathematical Physics Functional Analysis Operator Algebras |
| url | https://arxiv.org/abs/2503.03448 |