On a graded q-differential algebra

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作者
Abramov V. [1 ]
机构
[1] Institute of Pure Mathematics, University of Tartu, Tartu, 50409
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D O I
10.2991/jnmp.2006.13.s.1
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摘要
Given an associative unital ℤN-graded algebra over the complex numbers we construct the graded q-differential algebra by means of a graded q-commutator, where q is a primitive N-th root of unity. The N-differential d of the graded q-differential algebra is a homogeneous endomorphism of degree 1 satisfying the graded q-Leibniz rule and dN = 0. We apply this construction to a reduced quantum plane and study the exterior calculus on a reduced quantum plane induced by the N -differential of the graded q-differential algebra. Making use of the higher order differentials dkx induced by the N -differential d we construct an analogue of an algebra of differential forms with exterior differential satisfying dN = 0. © 2006 Taylor & Francis Group, LLC.
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页码:1 / 8
页数:7
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