ABNORMAL EXTREMALS OF LEFT-INVARIANT SUB-FINSLER QUASIMETRICS ON FOUR-DIMENSIONAL LIE GROUPS

We find the abnormal extremals on four-dimensional connected Lie groups with left-invariant sub-Finsler quasimetric defined by a seminorm on a two-dimensional subspace of the Lie algebra generating the algebra. In terms of the structure constants of a Lie algebra and the Minkowski support function of the unit ball of the seminorm on the two-dimensional subspace of a Lie algebra which defines a quasimetric, we establish a criterion for the strict abnormality of these extremals.