On Poincare Polinomials of Hyperbolic Lie Algebras

Abstract

Poincare polinomials of hyperbolic Lie algebras, which are given by $H{A}_2$ and $H{A}_3$ 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 $H{A}_2$ and $H{A}_3$.

7 pages, 5 figures, Plain TeX