Gang Han

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math.RA2025

A symmetric biderivation structure on polynomial algebras and a class of modules over the special Jordan algebra $H_{n} (K)$ of symmetric matrices

Yangjie Yin, Gang Han

There exists a biderivation structure on the polynomial algebra $A [n] = K [x_{1}, \dots, x_{n}],$ where $K$ is a field with $char (K) \neq = 2$ , defined by $f \circ h…

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…

A symmetric biderivation structure on polynomial algebras and a class of modules over the special Jordan algebra Hn​(K) of symmetric matrices

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

Normal forms of elements in the Weyl algebra and Dixmier Conjecture

Deformed Laurent series rings and completions of the Weyl division ring

A symmetric biderivation structure on polynomial algebras and a class of modules over the special Jordan algebra $H_{n} (K)$ of symmetric matrices