A class of Lie algebras arising from intersection matrices

Abstract

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.

Keywords

Intersection matrices / extended affine Lie algebra / generator / classification

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