Journal of Noncommutative Geometry

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Volume 12, Issue 3, 2018, pp. 865–887
DOI: 10.4171/JNCG/293

Published online: 2018-10-29

Bar simplicial modules and secondary cyclic (co)homology

Jacob Laubacher[1], Mihai D. Staic and Alin Stancu[2]

(1) Bowling Green State University, USA
(2) Columbus State University, USA

In this paper we study the simplicial structure of the complex $C^{\bullet}((A,B,\varepsilon); M)$, associated to the secondary Hochschild cohomology. The main ingredient is the simplicial object $\mathcal{B}(A,B,\varepsilon)$, 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).

Keywords: Hochschild cohomology, cyclic cohomology, simplicial k-modules

Laubacher Jacob, Staic Mihai, Stancu Alin: Bar simplicial modules and secondary cyclic (co)homology. J. Noncommut. Geom. 12 (2018), 865-887. doi: 10.4171/JNCG/293