Gravitation and Cosmology

, Volume 25, Issue 1, pp 18–23 | Cite as

Hidden Symmetries in a Mixmaster-Type Universe

  • A. E. PavlovEmail author


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 by a construction of the Cartan matrix of spacelike root vectors in Wheeler–DeWitt space. Kac-Moody algebras can be classified according to their Cartan matrix. In this way a hidden symmetry of the model considered is revealed. It is known that gravitational models which demonstrate a chaotic behavior are associated with hyperbolic Kac–Moody algebras. The algebra considered in our paper is not hyperbolic. The square of the Weyl vector is negative. The mixmaster-type universe is associated with a simply-laced Lorentzian Kac–Moody algebra. Since the volume of the billiard table is infinite, the model is not chaotic.


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© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Bogoliubov Laboratory for Theoretical PhysicsJoint Institute of Nuclear ResearchDubnaRussia
  2. 2.Institute of Mechanics and EnergeticsRussian State Agrarian University—Moscow Timiryazev Agricultural AcademyMoscowRussia

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