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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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Table of 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.