The study of redefinition of phases involves group cohomology. Two functions related as the hatted and non-hatted versions of above are said to be cohomologous. They belong to the same second cohomology class, i.e. they are represented by the same element in , the second cohomology group of . If an element of contains the trivial function , then it is said to be trivial. The topic can be studied at the level of Lie algebras and Lie algebra cohomology as well.