Special linear Lie ring:sl(2,2)

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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 Lie ring can be defined in the following equivalent ways:

\langle e,f,h \mid e + e = f + f = h + h = 0, [e,f] = h, [h,e] = [h,f] = 0 \rangle

  • It is the Lie ring of strictly upper-triangular 3 \times 3 matrices over the field of two elements, with the Lie bracket given by the commutator of two matrices [A,B] := AB - BA.

Arithmetic functions

Function Value Explanation
order of a Lie ring 8
nilpotency class of a Lie ring 2
derived length of a Lie ring 2
Frattini length of a Lie ring 2

Lie ring properties

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