A degree inequality for Lie algebras with a regular Poisson semi-center

TL;DR

This paper establishes a general bound on the sum of degrees of semi-invariants for Lie algebras with a polynomial Poisson semi-center, extending known results to a broader class.

Contribution

It provides a new, unified bound applicable to Lie algebras with polynomial Poisson semi-centers, generalizing previous special case results.

Findings

Bound for the sum of degrees of semi-invariants established

Applicable to Lie algebras with polynomial Poisson semi-center

Extends known results to a broader class

Abstract

For Lie algebras whose Poisson semi-center is a polynomial ring we give a bound for the sum of the degrees of the generating semi-invariants. This bound was previously known in many special cases.