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- W3046976307 abstract "We construct the Lie algebras of systems of $$2g$$ graded heat operators $$Q_0,Q_2,dots,Q_{4g-2}$$ that determine the sigma functions $$sigma(z,lambda)$$ of hyperelliptic curves of genera $$g=1$$, $$2$$, and $$3$$. As a corollary, we find that the system of three operators $$Q_0$$, $$Q_2$$, and $$Q_4$$ is already sufficient for determining the sigma functions. The operator $$Q_0$$ is the Euler operator, and each of the operators $$Q_{2k}$$, $$k>0$$, determines a $$g$$-dimensional Schrodinger equation with potential quadratic in $$z$$ for a nonholonomic frame of vector fields in the space $$mathbb C^{2g}$$ with coordinates $$lambda$$. For any solution $$varphi(z,lambda)$$ of the system of heat equations, we introduce the graded ring $$mathscr R_varphi$$ generated by the logarithmic derivatives of $$varphi(z,lambda)$$ of order $$ge 2$$ and present the Lie algebra of derivations of $$mathscr R_varphi$$ explicitly. We show how this Lie algebra is related to our system of nonlinear equations. For $$varphi(z,lambda)=sigma(z,lambda)$$, this leads to a well-known result on how to construct the Lie algebra of differentiations of hyperelliptic functions of genus $$g=1,2,3$$." @default.
- W3046976307 created "2020-08-10" @default.
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- W3046976307 date "2020-07-01" @default.
- W3046976307 modified "2023-10-16" @default.
- W3046976307 title "Lie Algebras of Heat Operators in a Nonholonomic Frame" @default.
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- W3046976307 doi "https://doi.org/10.1134/s0001434620070020" @default.
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