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.