math x yz zx z xy math math x math '' math math '' '' math z math '' math mathfrak g math using bilinearity expand lie bracket math x yx math using alternativity shows math xy yx math elements math x math '' math math '' math mathfrak g math showing bilinearity alternativity together imply anticommutativity math xy yx math elements math x math '' math math '' math mathfrak g math field 's characteristic anticommutativity implies alternativity since implies math xx xx math customary denote lie algebra lower case fraktur letter math mathfrak g
Formal science Mathematics Pure mathematics Algebra Lie algebra