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  • HOCHSCHILD (CO)HOMOLOGY OF ℤ2×ℤ2-GALOIS COVERINGS OF QUANTUM EXTERIOR ALGEBRAS

  • Part of
  • HOU BO, XU YUNGE
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 78 / Issue 1 / August 2008
    Published online by Cambridge University Press:
    01 August 2008, pp. 35-54
    Print publication:
    August 2008
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  • Let Aq=k〈x,y〉/(x2,xy+qyx,y2) be the quantum exterior algebra over a field k with , and let Λq be the ℤ2×ℤ2-Galois covering of Aq. In this paper the minimal projective bimodule resolution of Λq is constructed explicitly, and from it we can calculate the k-dimensions of all Hochschild homology and cohomology groups of Λq. Moreover, the cyclic homology of Λq can be calculated in the case where the underlying field is of characteristic zero.