# Dynkin Diagrams of Basic Lie Superalgebras

### From NZJM

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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 has many Dynkin diagrams, due to
different choices of simple root systems.
For with rank 4 or lower,
all its Dynkin diagrams have already been given explicitly.
To deal with with rank higher than 4,
this article introduces a combinatorial invariant on the
Dynkin diagrams.
It enables us to recognize 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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