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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.07021 |
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| _version_ | 1866929662480875520 |
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| author | de Santana, Adriano Baltazar, Rene Vinciguerra, Robson de Araujo, Wilian |
| author_facet | de Santana, Adriano Baltazar, Rene Vinciguerra, Robson de Araujo, Wilian |
| contents | Let $δ$ be a derivation in a $K$-algebra $R$ and let $Aut_δ(R)$ be the isotropy group with respect to the natural conjugation action of $Aut(R)$ of $K$-automorphisms on the set $Der(R)$ of $K$-derivations: that is, the subgroup of automorphisms that commute with the derivation. We explore the characterization of $Aut_δ(R)$ for quantum Weyl algebras and we prove that in the case of the Jordanian plane, with the inner part defined by a monomial, it is in general a subgroup of $\mathbb{Z}_t$. Furthermore, we obtain a necessary and sufficient condition for an automorphism to be in the isotropy group of any inner derivation in the Jordanian Plane. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_07021 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Isotropy Groups of Quantum Weyl Algebras and Jordanian Plane de Santana, Adriano Baltazar, Rene Vinciguerra, Robson de Araujo, Wilian Rings and Algebras Let $δ$ be a derivation in a $K$-algebra $R$ and let $Aut_δ(R)$ be the isotropy group with respect to the natural conjugation action of $Aut(R)$ of $K$-automorphisms on the set $Der(R)$ of $K$-derivations: that is, the subgroup of automorphisms that commute with the derivation. We explore the characterization of $Aut_δ(R)$ for quantum Weyl algebras and we prove that in the case of the Jordanian plane, with the inner part defined by a monomial, it is in general a subgroup of $\mathbb{Z}_t$. Furthermore, we obtain a necessary and sufficient condition for an automorphism to be in the isotropy group of any inner derivation in the Jordanian Plane. |
| title | On Isotropy Groups of Quantum Weyl Algebras and Jordanian Plane |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2407.07021 |