Dixmier conjecture
Encyclopedia
In algebra
the Dixmier conjecture, asked by , is the conjecture that any endomorphism
of a Weyl algebra is an automorphism.
showed that the Dixmier conjecture (generalized to Weyl algebras with more generators) is equivalent to the Jacobian conjecture
.
Algebra
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures...
the Dixmier conjecture, asked by , is the conjecture that any endomorphism
Endomorphism
In mathematics, an endomorphism is a morphism from a mathematical object to itself. For example, an endomorphism of a vector space V is a linear map ƒ: V → V, and an endomorphism of a group G is a group homomorphism ƒ: G → G. In general, we can talk about...
of a Weyl algebra is an automorphism.
showed that the Dixmier conjecture (generalized to Weyl algebras with more generators) is equivalent to the Jacobian conjecture
Jacobian conjecture
In mathematics, the Jacobian conjecture is a celebrated problem on polynomials in several variables. It was first posed in 1939 by Ott-Heinrich Keller...
.