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On Poincare Polinomials of Hyperbolic Lie Algebras

Hasan R. Karadayi·M. Gungormez
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Abstract

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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Hasan R. Karadayi, M. Gungormez. 2005-04-19. On Poincare Polinomials of Hyperbolic Lie Algebras. https://arxiv.org/abs/math-ph/0504061

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