Realizations of the Witt and Virasoro algebras and integrable equations
Realizations of the Witt and Virasoro algebras and integrable equations
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维特和维拉索罗代数和可积方程的实现
DOI：
10.1080/14029251.2020.1683964
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发表时间：
2020
影响因子：
0.7
通讯作者：
Renat Zhdanov
中科院分区：
文献类型：
--
作者：
Qing Huang;Renat Zhdanov
本文研究了无限维Witt代数和Virasoro代数的实现。我们得到了Witt代数在空间λ 3上由一阶微分算子的李向量场实现的完整描述。我们证明了它们都不允许非平凡的中心扩张，这意味着Virasoro代数在图3中不存在实现。本文描述了Witt代数的直和在环Lie向量场上的所有不等价实现。这一结果使得所有可能的（1+1）维偏微分方程，承认无穷维对称代数同构的Witt代数的直和的完整描述。用这种方法，我们构造了一类新的允许无穷维Witt代数的非线性偏微分方程。从而得到了新的允许无穷对称代数的可积模型。
In this paper we study realizations of infinite-dimensional Witt and Virasoro algebras. We obtain a complete description of realizations of the Witt algebra by Lie vector fields of first-order differential operators over the space ℝ3. We prove that none of them admits non-trivial central extension, which means that there are no realizations of the Virasoro algebra in ℝ3. We describe all inequivalent realizations of the direct sum of the Witt algebras by Lie vector fields over ℝ3. This result enables complete description of all possible (1+1)-dimensional partial differential equations that admit infinite dimensional symmetry algebras isomorphic to the direct sum of Witt algebras. In this way we have constructed a number of new classes of nonlinear partial differential equations admitting infinite-dimensional Witt algebras. So new integrable models which admit infinite symmetry algebra are obtained.