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The quantum de Rham complexes associated with \(SL_ h(2)\). (English) Zbl 0789.17010

Summary: Quantum de Rham complexes on the quantum plane and the quantum group itself are constructed for the nonstandard deformation of Fun(SL(2)). It is shown that in contrast to the standard \(q\)-deformation of SL(2), the above complexes are unique for \(\text{SL}_ h(2)\). Also, as a byproduct, a new deformation of the two-dimensional Heisenberg algebra is obtained which can be used to construct models of \(h\)-deformed quantum mechanics.

MSC:

17B37 Quantum groups (quantized enveloping algebras) and related deformations
16W30 Hopf algebras (associative rings and algebras) (MSC2000)
16S80 Deformations of associative rings
46L85 Noncommutative topology
46L87 Noncommutative differential geometry
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
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References:

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