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

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

2004-01-20

arxiv.org/abs/math/0401263v1

Mathematics

Rings and Algebras

23 pages

Scientific paper

For central simple finitely generated algebras of finite Gelfand-Kirillov dimension and for their division algebras upper bounds are obtained for the transcendence degree of their commutative subalgebras and subfields respectively. In the formulae for the upper bounds are used only two dimensions of the algebras: the Gelfand-Kirillov and the filter dimension. In the case of the ring of differential operators on a smooth irreducible affine algebraic variety the upper bounds are the exact upper bounds. A similar upper bound is given for the transcendence degree of isotropic subalgebras of strongly simple Poisson algebras.

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