Karimipour, Vahid The quantum de Rham complexes associated with \(SL_ h(2)\). (English) Zbl 0789.17010 Lett. Math. Phys. 30, No. 2, 87-98 (1994). 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. Cited in 13 Documents 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 Keywords:deformation of two-dimensional Heisenberg algebra; Cartan-Maurer forms; derivatives in noncommutative differential calculus; quantum plane; quantum group; nonstandard deformation of Fun(SL(2)) PDFBibTeX XMLCite \textit{V. Karimipour}, Lett. Math. Phys. 30, No. 2, 87--98 (1994; Zbl 0789.17010) Full Text: DOI arXiv References: [1] Takhtajan, L. A., in M. L. Ge and B. H. Zhao (eds),Introduction to Quantum Groups and Integrable Massive Models of Quantum Field Theory, World Scientific, Singapore, 1991. [2] Demidov, E. E., Manin, Yu. I., Mukhin, E. E., and Zhdanovich,Prog. Theor. Phys. Suppl. 102, 203-218 (1990). · doi:10.1143/PTPS.102.203 [3] Zakrzewski, S.,Lett. Math. Phys. 22, 287-289 (1991). · Zbl 0752.17018 · doi:10.1007/BF00405603 [4] Faddeev, L. D., Reshetikhin, N. Yu., and Takhtajan, L. A.,Leningrad Math. J. 1, 193-225 (1990). [5] Ohn, C. H.,Lett. Math. Phys. 25, 85-88 (1992). · Zbl 0766.17016 · doi:10.1007/BF00398304 [6] Manin, Yu., Bonn preprints MPI/91-47; MPI/91-60 (1991). [7] Wess, J. and Zumino, B.,Nuclear Phys. B (Proc. Supp.)18B, 302 (1990). · doi:10.1016/0920-5632(91)90143-3 [8] Woronowics, S. L.,Comm. Math. Phys. 122, 125 (1989). · Zbl 0751.58042 · doi:10.1007/BF01221411 [9] Aref’eva, I. Ya. and Volovich, I. V.,Phys. Lett. B 268, 179-188 (1991). · doi:10.1016/0370-2693(91)90801-V [10] Schwenk, J. and Wess, J.,Phys. Lett. B 291, 273-277 (1992). · doi:10.1016/0370-2693(92)91044-A [11] Schupp, P., Watts, P., and Zumino, B.,Lett. Math. Phys. 25, 139-147 (1992). · Zbl 0765.17020 · doi:10.1007/BF00398310 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.