mention some results and examples on rings with finite Gelfand -
Kirillov dimension, some open questions and results about extended
centers of algebras with quadratic growth with applications. In the
case when A is a finitely generated commutative algebra
Gelfand-Kirillov dimension is equal to Krull dimension. For this reason
Gelfand-Kirillov dimension is a useful tool for obtaining
noncommutative analogues of results from classical algebraic geometry.
Part of this talk is a joined work with Jason Bell and Tom Lenagan