Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 6 (2010), 040, 10 pages      arXiv:1003.2130      https://doi.org/10.3842/SIGMA.2010.040
Contribution to the Special Issue “Noncommutative Spaces and Fields”

Integral calculus on Eq(2)

Tomasz Brzeziński
Department of Mathematics, Swansea University, Singleton Park, Swansea SA2 8PP, UK

Received March 11, 2010; Published online May 13, 2010

Abstract
The complexes of integral forms on the quantum Euclidean group Eq(2) and the quantum plane are defined and their isomorphisms with the corresponding de Rham complexes are established.

Key words: integral forms; hom-connection; quantum Euclidean group.

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References

  1. Brzeziński T., Non-commutative connections of the second kind, J. Algebra Appl. 7 (2008), 557-573, arXiv:0802.0445.
  2. Brzeziński T., El Kaoutit L., Lomp C., Non-commutative integral forms and twisted multi-derivations, J. Noncommut. Geom. 4 (2010), 281-312, arXiv:0901.2710.
  3. Goodearl K.R., Letzter E.S., Prime ideals in skew and q-skew polynomial rings, Mem. Amer. Math. Soc. 109 (1994), no. 521, 106 pages.
  4. Krähmer U., Poincaré duality in Hochschild (co)homology, in New Techniques in Hopf Algebras and Graded Ring Theory, K. Vlaam. Acad. Belgie Wet. Kunsten (KVAB), Brussels, 2007, 117-125.
  5. Manin Yu.I., Gauge field theory and complex geometry, Grundlehren der Mathematischen Wissenschaften, Vol. 289, Springer-Verlag, Berlin, 1988.
  6. Penkov I.B., D-modules on supermanifolds, Invent. Math. 71 (1983), 501-512.
  7. Van den Bergh M., A relation between Hochschild homology and cohomology for Gorenstein rings, Proc. Amer. Math. Soc. 126 (1998), 1345-1348, Erratum, Proc. Amer. Math. Soc. 130 (2002), 2809-2810.
  8. Verbovetsky A., Differential operators over quantum spaces, Acta Appl. Math. 49 (1997), 339-361.
  9. Vinogradov M.M., Co-connections and integral forms, Russian Acad. Sci. Dokl. Math. 50 (1995), 229-233.
  10. Woronowicz S.L., Twisted SU(2) group. An example of a noncommutative differential calculus, Publ. Res. Inst. Math. Sci. 23 (1987), 117-181.
  11. Woronowicz S.L., Quantum SU(2) and E(2) groups. Contraction procedure, Comm. Math. Phys. 149 (1992), 637-652.

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