关于双曲李代数的Poincare多项式
On Poincare Polinomials of Hyperbolic Lie Algebras
摘要：
本文计算了双曲李代数的Poincare多项式，它们分别由Kac记法中的$HA_2$和$HA_3$给出.结果表明，双曲Poincare多项式存在一个有意义的形式。它们的显式形式往往被看作是一个适当选择的有限庞加莱多项式和多项式的有限程度的比率。为此，通过选择$D_4$和$D_5$李代数的Poincare多项式，我们证明了对于$HA_2$和$HA_3$，这些多项式分别是11阶和19阶的。
英文摘要：
Poincare polinomials of hyperbolic Lie algebras, which are given by $HA_2$ and $HA_3$ in the Kac's notation, are calculated explicitly. The results show that there is a significant form for hyperbolic Poincare polinomials. Their explicit forms tend to be seen as the ratio of a properly chosen finite Poincare polinomial and a polinomial of finite degree. To this end, by choosing the Poincare polinomials of $D_4$ and $D_5$ Lie algebras, we show that these polinomials come out to be of order 11 and 19 respectively for $HA_2$ and $HA_3$.
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