The Bianchi classification of the three-dimensional Lie algebras and of the spatially homogeneous universes is presented in a rather pedagogical manner. The dynamics of the Bianchi-I, Bianchi-II and Bianchi-IX universes are discussed in detail. A special attention is paid to the phenomenon of the oscillatory approach to the cosmological singularity (BKL) known also as the Mixmaster universe. The stochasticity in cosmology and the connection between cosmological billiards and infinite-dimensional Lie algebras are briefly illustrated.
CITATION STYLE
Kamenshchik, A. Y. (2019). The Bianchi Classification of the Three-Dimensional Lie Algebras and Homogeneous Cosmologies and the Mixmaster Universe. In Tutorials, Schools, and Workshops in the Mathematical Sciences (pp. 93–137). Birkhauser. https://doi.org/10.1007/978-3-030-18061-4_3
Mendeley helps you to discover research relevant for your work.