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arXiv · 1910.12950

Double-graded quantum superplane

Andrew James Bruce·Steven Duplij
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Abstract

A $\mathbb{Z}_2 \times \mathbb{Z}_2$-graded generalisation of the quantum superplane is proposed and studied. We construct a bicovariant calculus on what we shall refer to as the \emph{double-graded quantum superplane}. The commutation 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 $\mathbb{Z}_2^2$-algebra structure.

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BibTeXRIS

Andrew James Bruce, Steven Duplij. 2019-10-20. Double-graded quantum superplane. https://doi.org/10.1016/s0034-4877(20)30089-6

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