Complex sentence: In theories with supersymmetry, this definition can be generalized to include supergroups and Lie superalgebras and a central charge is any operator which commutes with all the other supersymmetry generators.
Split into simpler sentences: In theories with supersymmetry, this definition can be generalized to include supergroups and Lie superalgebras. A central charge is any operator which commutes with all the other supersymmetry generators.