Abstract.
We construct a q-analog of exterior calculus with a differential d satisfying d N = 0, where N ≥ 2 and q is a primitive Nth root of unity, on a noncommutative space and introduce a notion of a q-differential k-form. A noncommutative space we consider is a reduced quantum plane. Our construction of a q-analog of exterior calculus is based on a generalized Clifford algebra with four generators and on a graded q-differential algebra. We study the structure of the algebra of q-differential forms on a reduced quantum plane and show that the first order calculus induced by the differential d is a coordinate calculus. The explicit formulae for partial derivatives of this first order calculus are found.
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Abramov, V. Algebra Forms with \(d^{N} = 0\) on Quantum Plane. Generalized Clifford Algebra Approach. AACA 17, 577–588 (2007). https://doi.org/10.1007/s00006-007-0033-z
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DOI: https://doi.org/10.1007/s00006-007-0033-z