Corpus ID: 15029784

Kac-Moody Fibonacci sequences, hyperbolic golden ratios, and real quadratic fields

  title={Kac-Moody Fibonacci sequences, hyperbolic golden ratios, and real quadratic fields},
  author={K. K. Andersen and Lisa Carbone and D. Penta},
Let A be the generalized Cartan matrix of rank 2 Kac-Moody algebra g. We write g = g(a, b) when A has non-diagonal entries −a and −b. To each such A, its Weyl group and corresponding root lattice, we associate a ‘Fibonacci type ’ integer sequence. These sequences are derived from the coordinates of the real root vectors in the root space. Each element of each sequence can be expressed as a polynomial in the non-diagonal entries of the generalized Cartan matrix, whose coefficients are shallow… Expand
6 Citations

Tables from this paper


Rank 2 symmetric hyperbolic Kac-Moody algebras
  • 27
  • PDF
A hyperbolic GCM Lie algebra and the Fibonacci numbers
  • 31
  • PDF
The power of a prime that divides a generalized binomial coefficient.
  • 86
  • PDF
Advanced Number Theory
  • 209
  • PDF
Infinite-dimensional Lie algebras
  • 2,768
Factorization properties of chebyshev polynomials
  • 24
  • Highly Influential
  • PDF
On the Topology of Kac–Moody groups
  • 35
  • PDF
The statistics of dimers on a lattice: I. The number of dimer arrangements on a quadratic lattice
  • 881
Dimer problem in statistical mechanics-an exact result
  • 598
CRC Standard Mathematical Tables and Formulae
  • 459