Zhennan Pan

collaborators

3 papers

math.RA2025

Types of elements in non-commutative Poisson algebras and Dixmier Conjecture

Zhennan Pan, Gang Han

Non-commutative Poisson algebras are the algebras having an associative algebra structure and a Lie algebra structure together with the Leibniz law. Let $P$ be a non-commutative Po…

math.RA2024

Normal forms of elements in the Weyl algebra and Dixmier Conjecture

Gang Han, Zhennan Pan, Yulin Chen

A result of A. Joseph says that any nilpotent or semisimple element $z$ in the Weyl algebra $A_{1}$ over some algebracally closed field $K$ of characterstic 0 has a normal form up to…

math.RA2024

Deformed Laurent series rings and completions of the Weyl division ring

Gang Han, Yulin Chen, Zhennan Pan

Let $L ((T^{- 1}))$ be the space of (inverse) Laurent serieswith coefficients in some field $L$ . It has a standard degree map and the induced topology. With its usual addition and a…