Classification of minimal Z2×Z2-graded Lie (super)algebras and some applications

This paper presents the classification over fields of real and complex numbers, minimal Z2×Z2-graded Lie algebras superalgebras spanned by four generators with no empty graded sector. The inequivalent (super)algebras are obtained solving constraints imposed respective Jacobi identities. A motivation for this mathematical result is to systematically investigate properties dynamical systems invariant under (super)algebras. Recent works only paid attention special case one-dimensional Poincaré superalgebra. As applications, we able extend certain constructions originally introduced superalgebra other listed We mention, in particular, notion superspace (both classical worldline sigma models quantum Hamiltonians). a further by-product, point out that, contrary superalgebras, theory algebra implies presence ordinary bosons three different types exotic bosons, anticommuting among themselves.