Multiplicity-Free Gradings on Semisimple Lie and Jordan Algebras and Skew Root Systems  

作　　者：Gang Han Yucheng Liu Kang Lu 

机构地区：[1]Department of Mathematics, Zhejiang University, Hangzhou 310027, China

出　　处：《Algebra Colloquium》2019年第1期123-138,共16页代数集刊（英文版）

基　　金：The first author is supported by Zhejiang Province Science Foundation (grant No. LY14A010018).

摘　　要：A G-grading on an algebra, where G is an abelian group, is called multiplicityfree if each homogeneous component of the grading is 1-dimensional. We introduce skew root sys tems of Lie type and skew root systems of Jordan type, and use them to cons true t multiplicity-free gradings on semisimple Lie algebras and on semisimple Jordan algebras respectively. Under certain conditions the corresponding Lie (resp., Jordan) algebras are simple. Two families of skew root systems of Lie type (resp., of Jordan type) are constructed and the corresponding Lie (resp., Jordan) algebras are identified. This is a new approach to study abelian group gradings on Lie and Jordan algebras.

关 键 词：multiplicity-free grading symplectic abelian group SKEW root system SIMPLE LIE ALGEBRA SIMPLE Jordan ALGEBRA 

分 类 号：O1[理学—数学]