Dynkin Diagrams of Basic Lie Superalgebras


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New Zealand Journal of Mathematics

Vol. 41, (2011), Pages 55-64

Ching-I Hsin

Department of Computer Science and Information Engineering,

Minghsin University of Science and Technology,


Abstract A basic Lie superalgebra Image:frakg.png has many Dynkin diagrams, due to different choices of simple root systems. For Image:frakg.png with rank 4 or lower, all its Dynkin diagrams have already been given explicitly. To deal with Image:frakg.png with rank higher than 4, this article introduces a combinatorial invariant on the Dynkin diagrams. It enables us to recognize Image:frakg.png from a given Dynkin diagram. In this way, we obtain all the Dynkin diagrams of any given basic Lie superalgebra.

Keywords basic Lie superalgebra, Dynkin diagram, simple system

Classification (MSC2000) 17B20, 17B05, 05C15.

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