ℤ2 × ℤ2-graded Lie algebras and supseralgebras and related physical models

Abstract

Abstract In this paper we construct physical systems with ℤ2×ℤ2-graded symmetries. There are two different structures:ℤ2×ℤ2-graded Lie algebras andℤ2×ℤ2-graded Lie superalgebras. Physical models with the latter symmetries can be seen as generalizations of supersymmetric models. The systems described by ℤ2 × ℤ2-graded Lie algebras have not been investigated yet (up to our knowledge). We present examples of physical models invariant under each one of both kinds of graded structures.