Tensor Products of Algebras and Their Applications to the Construction of Anosov Diffeomorphisms

In this paper, we develop algebraic approaches to the construction of Anosov diffeomorphisms on compact manifolds. Two mutually dual constructions are described, which provide numerous new examples of Anosov diffeomorphisms on nilmanifolds. The basis of the constructions is the operation of tensor multiplication of Lie algebras by appropriate finite-dimensional associative-commutative algebras. Several examples illustrating the general method are given.