Hidden Symmetries in a Mixmaster-Type Universe

Abstract

A model of multidimensional mixmaster-type vacuum universe is considered. It belongs to a class of pseudo-Euclidean chains characterized by root vectors. An algebraic approach of our investigation is founded on construction of Cartan matrix of the spacelike root vectors in Wheeler -DeWitt space. Kac -Moody algebras can be classified according to their Cartan matrix. By this way a hidden symmetry of the model considered is revealed. It is known, that gravitational models which demonstrate chaotic behavior are associated with hyperbolic Kac -Moody algebras. The algebra considered in our paper is not hyperbolic. The square of Weyl vector is negative. The mixmaster-type universe is associated with a simply-laced Lorentzian Kac -Moody algebra. Since the volume of the configuration space is infinite, the model is not chaotic.