Gelfand-Kirillov dimension of commutative subalgebras of simple infinite dimensional algebras and their quotient division algebras

摘要

For central simple finitely generated algebras of finite Gelfand-Kirillovdimension and for their division algebras upper bounds are obtained for thetranscendence degree of their commutative subalgebras and subfieldsrespectively. In the formulae for the upper bounds are used only two dimensionsof the algebras: the Gelfand-Kirillov and the filter dimension. In the case ofthe ring of differential operators on a smooth irreducible affine algebraicvariety the upper bounds are the exact upper bounds. A similar upper bound isgiven for the transcendence degree of isotropic subalgebras of strongly simplePoisson algebras.