Poincare Polinomials of Hyperbolic Lie Algebras of Rank Three

TL;DR

This paper explicitly computes the Poincare polynomials for 19 hyperbolic Lie algebras of rank three, revealing a pattern where each polynomial is a ratio involving the Poincare polynomial of B3 and a finite-degree polynomial.

Contribution

It provides explicit formulas for the Poincare polynomials of 19 hyperbolic Lie algebras of rank three, extending previous work and identifying a common ratio form.

Findings

Each polynomial is expressed as a ratio involving the Poincare polynomial of B3.

The Poincare polynomials of these hyperbolic Lie algebras follow a specific ratio pattern.

The work enhances understanding of the structure of hyperbolic Lie algebras of rank three.

Abstract

In view of a previous work, we explicitly give the Poincare polinomials of 19 Hyperbolic Lie algebras of rank 3. It is seen that every one of these polinomials is expressed as the ratio of Poincare polinomial of $B_3$ Lie algebra and a polinomial of finite degree.