Special linear Lie ring:sl(2,3)

This article is about a particular Lie ring, viz., a Lie ring unique upto isomorphism
View a complete list of particular Lie rings

Definition

This is the special linear Lie ring of degree two over the field of three elements. In other words, it s the Lie ring of $2\times 2$ matrices of trace zero over the field of three elements, where the Lie bracket of two matrices $A$ and $B$ is $AB-BA$.

Arithmetic functions

Function	Value	Explanation
order	27
exponent	3

Lie ring properties

Property	Satisfied	Explanation
abelian Lie ring	No
nilpotent Lie ring	No
solvable Lie ring	No
simple Lie ring	Yes