  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.
