The Jacobian algebras

Vladimir Bavula (Sheffield)

Wednesday 23rd April, 2008 16:00-17:00 214

Abstract

The Jacobian algebras are obtained from the Weyl algebras by inverting (not in the sense of Ore) of certain elements. Surprisingly, the Jacobian algebras and the Weyl algebras have little in common. Moreover, they have almost opposite properties. The Jacobian algebras appeared in my study of the group of polynomial automorphisms and the Jacobian Conjecture, which is a conjecture that makes sense only for polynomial algebras in the class of all commutative algebras. In order to solve the Jacobian Conjecture, it is reasonable to believe that one should create technique which makes sense only for polynomials; the Jacobian algebras are a step in this direction (they exist for polynomials but make no sense even for Laurent polynomials).

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