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Gelfand-Kirillov dimension of commutative subalgebras of simple infinite dimensional algebras and their quotient division algebras by V. Bavula is a Mathematics article available to read on EtoBox.

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Let Q m 1⁄4 Kðx 1 ; . . . ; x m Þ be a rational function field (of transcendence degree m) over a field K. The following two inequalities are main results of the paper. ## : Let X be a smooth irreducible a‰ne algebraic variety of dimension n > 0 over an algebraically closed field K of characteristic zero. For the ring of di¤erential operators A 1⁄4 DðX Þ on X and for its quotient division ring B 1⁄4 DðX Þ the right hand sides of the inequalities (both are equal to n) are the exact upper bounds for the Gelfand-Kirillov dimensions of commutative subalgebras in DðX Þ and for the transcendence degrees of subfields in DðX Þ respectively. A similar upper bound is obtained for the Gelfand-Kirillov dimension of isotropic subalgebras of strongly simple Poisson algebras.

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Author

V. Bavula

Publisher

Walter de Gruyter GmbH

Published

2005

Field

Mathematics (Physical Sciences)