Journal of Generalized Lie Theory and Applications

ISSN: 1736-4337

Open Access

On Poincare Polynomials of Hyperbolic Lie Algebras


Gungormez M and Karadayi HR

We have general frameworks to obtain Poincare polynomials for Finite and also Affine types of Kac-Moody Lie algebras. Very little is known however beyond Affine ones, though we have a constructive theorem which can be applied both for finite and infinite cases. One can conclusively said that theorem gives the Poincare polynomial P(G) of a Kac-Moody Lie algebra G in the product form P(G)=P(g) R where g is a precisely chosen sub-algebra of G and R is a rational function. Not in the way which theorem says but, at least for 48 hyperbolic Lie algebras considered in this work, we have shown that there is another way of choosing a sub-algebra in such a way that R appears to be the inverse of a finite polynomial. It is clear that a rational function or its inverse can not be expressed in the form of a finite polynomial.

Our method is based on numerical calculations and results are given for each and every one of 48 Hyperbolic Lie algebras.

In an illustrative example however, we will give how above-mentioned theorem gives us rational functions in which case we find a finite polynomial for which theorem fails to obtain.


Share this article

50+ Million Readerbase

Journal Highlights

Google Scholar citation report
Citations: 1926

Journal of Generalized Lie Theory and Applications received 1926 citations as per Google Scholar report

Journal of Generalized Lie Theory and Applications peer review process verified at publons

Indexed In

arrow_upward arrow_upward