############################################################################# ## #D $2.A_6$ as $2 \times 2$ matrices over the quaternions over $\Q( r_3 )$ ## local result, r3, gens, e, i, alpha; result:= rec(); result.comment:= "2.A6 as 2x2 matrices over the quaternions over Q( r3 ).\n\ "; r3:= ER(3); gens:= GeneratorsOfAlgebra( QuaternionAlgebra( Field( r3 ) ) );; e:= gens[1]; i:= gens[2]; alpha:= r3/6 * gens[3]; result.generators:= [ [ [ 2*(e-i)*alpha, -e/2 - alpha ], [ e/2 - alpha, -i*(e/2-alpha) - 2*alpha ] ], [ [ 0*e, -e ], [ i, 0*e ] ] ]; return result;