Graphs and the (co)homology of Lie algebras

In this paper, we develop a diamond graph theory and apply the theory to the (co)homology of the Lie algebra generated by positive systems of the classical semi-simple Lie algebras over the field of complex numbers. As an application, we give the weight decomposition of the diamond Lie algebra with...

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Bibliographic Details
Published in:arXiv.org 2011-07
Main Author: Zheng, Qibing
Format: Article
Language:English
Subjects:
Algebra
Complex numbers
Diamonds
Fields (mathematics)
Graph theory
Homology
Lie groups
Quantum theory
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Summary:In this paper, we develop a diamond graph theory and apply the theory to the (co)homology of the Lie algebra generated by positive systems of the classical semi-simple Lie algebras over the field of complex numbers. As an application, we give the weight decomposition of the diamond Lie algebra with Dynkin graph \(A_{n+1}\) and compute the rank of every weight subgraph of it.
ISSN:2331-8422