Year: 2026
Type: preprint
Abstract: We study the commuting scheme of the exceptional Lie algebra $\mathfrak{g}_2$ via computational methods. Over a field of characteristic zero, we show that the commuting scheme of $\mathfrak{g}_2$ is reduced, Cohen-Macaulay and normal. Our computations give an explicit homogeneous system of parameters, determine the Hilbert series and degree, identify the first syzygies of the commuting ideal and show that it is not Gorenstein. We extend some of the above results to positive characteristic.
Source: arXiv (Cornell University)
Author: Goyal, Pallav
Institution: University of Southern Denmark
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220663909