Eugeny Chibrikov
Novosibirsk Technical University, Novosibirsk, Russia
Sabinin Algebras.
Abstract: One of the most important results in mathematics is the correspondence between Lie algebras and local Lie groups. The Sabinin algebra is a broad generalization of Lie algebras, it was defined by geometricians L.V.Sabinin and P.O.Miheev as an algebraic structure on the tangent space of any analytic loop so that Lie correspondence holds. The study of Sabinin algebras is essential for applications to differential geometry, mathematical physics, Poisson and symplectic mechanics, quantum gravity and etc. In the project we are going to study free Sabinin algebras and problems connected with free algebras. We plan to investigate linear bases of a free Sabinin algebra which is very important for further development of the Sabinin algebra theory. To achieve this goal, we will combine the techniques developed in the theories of Lie (super)algebras and conformal Lie algebras. The second objective of the project is to find an answer to the question about freedom of subalgebras of a free Sabinin algebra. We plan to apply in this part the methods of free Lie (super)algebras, free nonassociative algebras and free Akivis algebras.