• Corpus ID: 119166229

Fine gradings of complex simple Lie algebras and Finite Root Systems

  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},
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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