Quantum de Rham complex with $d^3 = 0$ differential

Details Quantum de Rham complex with $d^3 = 0$ differential Quantum de Rham complex with $d^3 = 0$ differential

2001-10-03

arxiv.org/abs/math-ph/0110007v3

Czech. J. Phys., 51 2001 1266

Physics

Mathematical Physics

6 pages, submitted to Czechoslovak Journal of Physics v. 51 (2001)

Scientific paper

10.1023/A:1013301532095

In this work, we construct the de Rham complex with differential operator d satisfying the Q-Leibniz rule, where Q is a complex number, and the condition $d^3=0$ on an associative unital algebra with quadratic relations. Therefore we introduce the second order differentials $d^2x^i$. In our formalism, besides the usual two-dimensional quantum plane, we observe that the second order differentials $d^2 x$ and $d^2 y$ generate either bosonic or fermionic quantum planes, depending on the choice of the differentiation parameter Q.

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