论文标题
Schrödinger操作员的Sigma功能和谎言代数
Sigma functions and Lie algebras of Schrödinger operators
论文作者
论文摘要
在V. M. Buchstaber和D. V. Leikin的工作中，对于任何$ g> 0 $，定义了一个具有二次电势的磁场的$ 2G $多维Schrödinger方程的系统。该系统等效于非体力学框架中的热方程系统。事实证明，这样的系统决定了$ g $属的通用性透明曲线的Sigma功能。介绍了一个多项式LIE代数，$ 2G $Schrödinger运营商$ q_0，q_2，\ ldots，q_ {4g-2} $作为发电机。 In this work for any $g > 0$ we obtain explicit expressions for $Q_0$, $Q_2$, $Q_4$, and recurrent formulas for $Q_{2k}$ with $k>2$ expressing this operators as elements of the polynomial Lie algebra using Lie brackets of the operators $Q_0$, $Q_2$, and $Q_4$. 作为一个应用程序，我们获得了操作员的明确表达式$ q_0，q_2，\ ldots，q_ {4g-2} $ for $ g = 1,2,3,4 $。
In the work by V. M. Buchstaber and D. V. Leikin for any $g > 0$ is defined a system of $2g$ multidimensional Schrödinger equations in magnetic fields with quadratic potentials. This systems are equivalent to systems of heat equations in nonholonomic frame. It is proved that such a system determines the sigma function of the universal hyperelliptic curve of genus $g$. A polynomial Lie algebra with $2g$ Schrödinger operators $Q_0, Q_2, \ldots, Q_{4g-2}$ as generators was introduced. In this work for any $g > 0$ we obtain explicit expressions for $Q_0$, $Q_2$, $Q_4$, and recurrent formulas for $Q_{2k}$ with $k>2$ expressing this operators as elements of the polynomial Lie algebra using Lie brackets of the operators $Q_0$, $Q_2$, and $Q_4$. As an application we obtain explicit expressions for the operators $Q_0, Q_2, \ldots, Q_{4g-2}$ for $g = 1,2,3,4$.
