This paper introduces the parastatistics induced by ${\mathbb {Z}} _ {2}{\times}{\mathbb {Z}}
_ {2}-\mathrm {g}\mathrm {r}\mathrm {a}\mathrm {d}\mathrm {e}\mathrm {d} $ algebras. It …

We construct classes of Z 2× Z 2-graded Lie algebras corresponding to the classical Lie
algebras in terms of their defining matrices. For the Z 2× Z 2-graded Lie algebra of type A …

In a previous paper we introduced the notion of Z 2× Z 2-graded classical mechanics and
presented a general framework to construct, in the Lagrangian setting, the worldline sigma …

Abstract Z _2 * Z _2 Z 2× Z 2-graded mechanics admits four types of particles: ordinary
bosons, two classes of fermions (fermions belonging to different classes commute among …

The superalgebra of ℤ 2 2-graded supersymmetric quantum mechanics is shown to be
realizable in terms of a single bosonic degree of freedom. Such an approach is directly …

In the recent paper (Bruce and Duplij 2019 (arXiv: 1904.06975 [math-ph])), Bruce and Duplij
introduced a double-graded version of supersymmetric quantum mechanics (SQM). It is an …

This paper presents the classification over the fields of real and complex numbers, of the
minimal Z 2× Z 2-graded Lie algebras and Lie superalgebras spanned by four generators …

We investigate superfield formulation of the minimal Z 2 2-supersymmetry. It is shown that
the integrability on Z 2 2-superspace guarantees the invariance of action. Then we present …

A novel feature of the Z 2× Z 2-graded supersymmetry which finds no counterpart in ordinary
supersymmetry is the presence of 11-graded exotic bosons (implied by the existence of two …

It is shown that the N= 1 supersymmetric quantum mechanics (SQM) can be extended to a Z
2 n-graded superalgebra. This is done by presenting quantum mechanical models that …