References of "Duplij, Steven"
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See detailDouble-Graded Quantum Superplane
Bruce, Andrew UL; Duplij, Steven

in Reports on Mathematical Physics (2020), 86(3), 383-400

A ℤ2 × ℤ2-graded generalisation of the quantum superplane is proposed and studied. We construct a bicovariant calculus on what we shall refer to as the double-graded quantum superplane. The ommutation ... [more ▼]

A ℤ2 × ℤ2-graded generalisation of the quantum superplane is proposed and studied. We construct a bicovariant calculus on what we shall refer to as the double-graded quantum superplane. The ommutation rules between the coordinates, their differentials and partial derivatives are explicitly given. Furthermore, we show that an extended version of the double-graded quantum superplane admits a natural Hopf -algebra structure. [less ▲]

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See detailDouble-Graded Supersymmetric Quantum Mechanics
Bruce, Andrew UL; Duplij, Steven

in Journal of Mathematical Physics (2020), 61

A quantum mechanical model that realizes the ℤ2×ℤ2-graded generalization of the one-dimensional supertranslation algebra is proposed. This model shares some features with the well-known Witten model and ... [more ▼]

A quantum mechanical model that realizes the ℤ2×ℤ2-graded generalization of the one-dimensional supertranslation algebra is proposed. This model shares some features with the well-known Witten model and is related to parasupersymmetric quantum mechanics, though the model is not directly equivalent to either of these. The purpose of this paper is to show that novel "higher gradings" are possible in the context of non-relativistic quantum mechanics. [less ▲]

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