# Fine gradings of complex simple Lie algebras and Finite Root Systems

@article{Han2014FineGO, title={Fine gradings of complex simple Lie algebras and Finite Root Systems}, author={Gang Han and Kang Lu and Jun Yu}, journal={arXiv: Group Theory}, year={2014} }

A $G$-grading on a complex semisimple Lie algebra $L$, where $G$ is a finite abelian group, is called quasi-good if each homogeneous component is 1-dimensional and 0 is not in the support of the grading.
Analogous to classical root systems, we define a finite root system $R$ to be some subset of a finite symplectic abelian group satisfying certain axioms. There always corresponds to $R$ a semisimple Lie algebra $L(R)$ together with a quasi-good grading on it. Thus one can construct nice basis…

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