Integrable spinning extension of a free particle on $$ \mathcal{S} $$2 is constructed in which spin degrees of freedom are represented by a 3-vector obeying the Bianchi type-V algebra. Generalizations involving a scalar potential giving rise to two quadratic constants of the motion, or external field of the Dirac monopole, or the motion on the group manifold of SU(2) are built. A link to the model of a relativistic spinning particle propagating on the near horizon 7d Myers-Perry black hole background is considered. Implications of the construction in this work for the D(2, 1; α) superconformal mechanics are discussed.

中文翻译：

---

S$$ \mathcal{S} $$2 上的 Bianchi V 型旋转粒子

$$ \mathcal{S} $$2 上自由粒子的可积自旋扩展被构造，其中自旋自由度由服从 Bianchi V 型代数的 3 向量表示。建立涉及引起运动的两个二次常数、或狄拉克单极子的外场或SU(2)的群流形上的运动的标量势的推广。考虑到在近地平线 7d Myers-Perry 黑洞背景上传播的相对论自旋粒子模型的链接。讨论了这项工作中的构造对 D(2, 1; α) 超共形力学的影响。