vector field ''x'' first order partial differential operator ''l'' sub ''x'' sub acting smooth functions letting ''l'' sub ''x'' sub ''f'' directional derivative function ''f'' direction ''x'' lie bracket ''x''''y'' two vector fields vector field defined action functions formula math l xy f l x l f l l x f math kac moody algebras large class infinite dimensional lie algebras whose structure similar finite dimensional cases moyal algebra infinite dimensional lie algebra contains classical lie algebras subalgebras virasoro algebra paramount importance
Formal science Mathematics Pure mathematics Algebra Lie algebra