Abstract
By using the first and second flows of the Kowalevski top, we can recreate the Kowalevski top into two−flows Kowalevski top, which has two−time variables. Then, we demonstrate that equations of the two−flows Kowalevski top become those of the full genus two Jacobi inversion problem. In addition to the Lax pair for the first flow, we construct a Lax pair for the second flow. Using the first and second flows, we demonstrate that the Lie group structure of these two Lax pairs is Sp(4, )/. With the two−flows Kowalevski top, we can conclude that the Lie group structure of the genus two hyperelliptic function is Sp(4, )/.
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