2014/10/29 by Gang Han, Kang Lu, Han, Gang +3
Biochemistry, Genetics and Molecular Biology · Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT) #Sphingolipid Metabolism and Signaling #math.GR #math.RT
paper · pdf · doi:10.48550/arxiv.1410.7945
arxiv created 2014/10/29 · openalex publication_date 2014/10/29 · arxiv updated 2014/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 of L(R) by means of finite root systems. We classify finite maximal abelian subgroups T in \Aut(L) for complex simple Lie algebras L such that the grading induced by the action of T on L is quasi-good, and show that the set of roots of T in L is always a finite root system. There are five series of such finite maximal abelian subgroups, which occur only if L is a classical simple Lie algebra.