Frontiers of Mathematics in China >

2015 , Vol. 10 >Issue 1: 185 - 198

DOI: https://doi.org/10.1007/s11464-014-0418-y

RESEARCH ARTICLE

A class of Lie algebras arising from intersection matrices

  • Li-meng XIA , 1 ,
  • Naihong HU 2
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  • 1. Faculty of Science, Jiangsu University, Zhenjiang 212013, China
  • 2. Department of Mathematics, East China Normal University, Shanghai 200241, China

Received date: 09 May 2013

Accepted date: 19 Jul 2014

Published date: 30 Dec 2014

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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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.

Key words： Intersection matrices; extended affine Lie algebra; generator; classification

Cite this article

Li-meng XIA , Naihong HU . A class of Lie algebras arising from intersection matrices[J]. Frontiers of Mathematics in China, 2015 , 10(1) : 185 -198 . DOI: 10.1007/s11464-014-0418-y

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