A class of Lie algebras arising from intersection matrices

TL;DR

This paper introduces a new class of Lie algebras derived from symmetrizable generalized intersection matrices, distinct from existing classes, and classifies them using modified Dynkin diagrams.

Contribution

It defines a novel class of Lie algebras from symmetrizable matrices and provides a classification method via modified Dynkin diagrams.

Findings

New class of Lie algebras from symmetrizable matrices

Distinct from generalized intersection matrix algebras

Classified by modified Dynkin diagrams

Abstract

In present work, we find a class of Lie algebras, which are defined from the symmetrizable generalized intersection matrices. However, such algebras are different from generalized intersection matrix algebras and intersection matrix algebras. Moreover, such Lie algebras generated by semi-positive definite matrices can be classified by the modified Dynkin diagrams.