Wednesday February 11, 2015
Ivan Shestakov, University of Sao Paulo

The Freiheitssatz  for generic Poisson algebras


A generic Poisson algebra is a commutative associative algebra with an anticommutative product (a bracket), which satisfies the Leibnitz identity but, in general,  does not satisfy the Jacobi identity. We prove that the Freiheitssatz holds in the variety of generic Poisson algebras. In other words, every non-trivial equation over the free generic Poisson algebra P has a solution in some extension of P. Earlier this result was proved for ordinary Poisson algebras by L.Makar Limanov and U.Umirbaev. This is a joint work with P. Kolesnikov and L. Makar Limanov.