-Orderings and -valuations on algebras of finite Gelfand–Kirillov dimension

The paper considers the real *-spectrum of a finitely generated algebra with involution over C of finite Gelfand-Kirillov dimension. It is showN that for such an algebra the stability indices associated to the real *-spectrum are bounded by the Gelfand-Kirillov dimension, as in the commutative case, and results on minimal generation of constructible sets in the real *-spectrum carry over. Birkhoff-Witt algebras of finite dimensional Lie algebras with involution are examples of such algebras. The real *-spectrum of a Brikhoff-Witt algebra is examined in detail in the 2-dimensional case.