JournalsjncgVol. 12, No. 3pp. 865–887

Bar simplicial modules and secondary cyclic (co)homology

  • Jacob Laubacher

    Bowling Green State University, USA
  • Mihai D. Staic

    Bowling Green State University, USA and Romanian Academy, Bucharest, Romania
  • Alin Stancu

    Columbus State University, USA
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Abstract

In this paper we study the simplicial structure of the complex C((A,B,ε);M)C^{\bullet}((A,B,\varepsilon); M), associated to the secondary Hochschild cohomology. The main ingredient is the simplicial object B(A,B,ε)\mathcal{B}(A,B,\varepsilon), which plays a role equivalent to that of the bar resolution associated to an algebra. We also introduce the secondary cyclic (co)homology and establish some of its properties (Theorems 4.11 and 5.11).

Cite this article

Jacob Laubacher, Mihai D. Staic, Alin Stancu, Bar simplicial modules and secondary cyclic (co)homology. J. Noncommut. Geom. 12 (2018), no. 3, pp. 865–887

DOI 10.4171/JNCG/293