Quantum de Rham complex with d3 = 0 differential*)

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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 d3=0 on an associative unital algebra with quadratic relations. Therefore we introduce the second order differentials d2xi. In our formalism, besides the usual two-dimensional quantum plane, we observe that the second order differentials d2x and d2x generate either bosonic or fermionic quantum planes, depending on the choice of the differentiation parameter Q.

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