Special linear Lie ring:sl(2,2)

Definition
This Lie ring can be defined in the following equivalent ways:


 * It is the special linear Lie ring of degree two over the field of two elements: the Lie ring of $$2 \times 2$$ matrices of trace zero over the field of two elements. It is defined by the following presentation:

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


 * 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 $$[A,B] := AB - BA$$.