Extended Classical Conformal Algebras and the Second Hamiltonian Structure of Lax Equations
Extended Classical Conformal Algebras and the Second Hamiltonian Structure of Lax Equations
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DOI：
10.1016/0370-2693(88)91211-7
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发表时间：
1988-07
影响因子：
4.4
通讯作者：
P. Mathieu
中科院分区：
文献类型：
--
作者：
P. Mathieu
证明了扩展的经典共形代数，即n>2的自旋代数，可以从n阶Lax算子的Lax方程的第二Hamilton结构中得到，即L（n）= xn+Σi= 0 n-2ui xi。这是Korteweg-de弗里斯方程和Virasoro代数（n=2）之间关系的自然推广。经典的自旋-3代数就是这样导出的。对自旋-4代数和最低半整数自旋代数（32和52）也作了一些讨论。
It is shown that extended classical conformal algebras, that is n>2 spin algebras, can be obtained from the second hamiltonian structure of Lax equations for a Lax operator of order n, i.e. L(n)=∂xn+Σi=0n−2ui∂xi. This is the natural generalization of the relation previously found between the Korteweg-de Vries equation and the Virasoro algebra (n=2). The classical spin-3 algebra is derived in this way. Some remarks on the spin-4 algebra and on the lowest half-integer spin algebras (3 2 and 5 2 ) are also presented.