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Quantum Simulation Entanglement Theory Quantum Correlations

Double-graded quantum superplane

arXiv

Authors: Andrew James Bruce, Steven Duplij

Year

2019

Paper ID

15433

Status

Preprint

Abstract Read

~2 min

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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 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}₂²-algebra structure.

Why This Paper Matters

This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
It adds a 2019 reference point for readers tracking recent quantum research.
A mathbbZ2 times mathbbZ2-graded generalisation of the quantum superplane is proposed and studied.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1910.12950 [2] arXiv https://arxiv.org/abs/1910.12950 [3] Publisher https://arxiv.org/abs/1910.12950

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