Hamilton李超代数的Borel子代数

设H(n)(n≥5)为复数域上秩为n的有限维Hamilton单李超代数.通过对正则元的分类,得到H(n)(n=5,6,7)关于典范环面的所有正根系,从而通过确定单根系得到正根系的连接关系,进而得到所有的Borel子代数及其连接关系.证明了H(n)(n≥5)的所有Borel子代数都不是极大可解的子代数.

Borel Subalgebras of Hamilton Lie Superalgebras

Let H(n)(n≥5) be a finite-dimensional simple Hamilton Lie superalgebra of rank n over the field of complex numbers C.In the paper,we first characterize all the positive root systems of H(n)(n = 5,6,7) with respect to the standard torus by mean.s.of classifying all the regular elements and in particular we obtain all the Borel subalgebras with respect to the canonical torus.Then,we determine all the simple root systems and describe the connection relations between the Borel subalgebras.We also prove that all the Borel subalgebras of H(n) with n≥ 5 are not maximal solvable subalgebras.