Realization by linear vector fields is constructed for any Lie algebra which admits a biorthogonal system and for its any suitable representation. The embedding into Lie algebras of linear vector fields is analogous to the classical Jordan-Schwinger map. A number of examples of such Lie algebras of linear vector fields is computed. In particular, we obtain examples of the twisted Heisenberg-Virasoro Lie algebra and the Schrodinger-Virasoro Lie algebras among others. More generally, we construct an embedding of an arbitrary locally convex topological algebra into the Cuntz algebra.

中文翻译：

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通过线性向量场和 Cuntz 代数的凸拓扑代数

线性向量场的实现是为任何允许双正交系统的李代数及其任何合适的表示构建的。线性向量场到李代数的嵌入类似于经典的 Jordan-Schwinger 映射。计算了线性向量场的这种李代数的许多示例。特别是，我们获得了扭曲的海森堡-维拉索罗李代数和薛定谔-维拉索罗李代数等的例子。更一般地说，我们将任意局部凸拓扑代数嵌入到 Cuntz 代数中。