Classification of Certain Regular Subalgebras of $\mathfrak{sl}(n, \mathbb C)$ up to Conjugacy

Shreya Dhar

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arXiv · 2406.17833

Classification of Certain Regular Subalgebras of $\mathfrak{sl}(n, \mathbb C)$ up to Conjugacy

Shreya Dhar

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Abstract

In this paper we will be classifying some regular upper-triangular subalgebras of $\mathfrak{sl}(n, \mathbb C)$ up to conjugacy by matrices in $SL(n, \mathbb C)$. We do so for dimension 2, codimension 1, and codimension 2 subalgebras. We prove some general results for codimension $k$. The approach we use reduces an abstract classification problem to a combinatorial one, which we solve through a mixture of inductive and computational approaches.

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BibTeX RIS

Shreya Dhar. 2024-06-25. Classification of Certain Regular Subalgebras of $\mathfrak{sl}(n, \mathbb C)$ up to Conjugacy. https://arxiv.org/abs/2406.17833

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