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Double-graded quantum superplane

Quantum Algebra 2020-12-30 v3 High Energy Physics - Theory Mathematical Physics math.MP Quantum Physics

Abstract

A Z2×Z2\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 Z22\mathbb{Z}_2^2-algebra structure.

Keywords

Cite

@article{arxiv.1910.12950,
  title  = {Double-graded quantum superplane},
  author = {Andrew James Bruce and Steven Duplij},
  journal= {arXiv preprint arXiv:1910.12950},
  year   = {2020}
}

Comments

20 pages, amslatex, romp.sty, version 3: final journal version, to appear in "Reports on Mathematical Physics"

R2 v1 2026-06-23T11:57:42.711Z