Hopf-cyclic coefficients in the braided setting

  • Ilya Shapiro

    University of Windsor, Canada
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Abstract

Considering the monoidal category obtained as modules over a Hopf algebra in a rigid braided category , we prove decomposition results for the Hochschild and cyclic homology categories and of . This is accomplished by defining a notion of a (stable) anti-Yetter–Drinfeld module with coefficients in a (stable) braided module over . When the stable braided module is , we recover and . The decomposition of now follows from that of .

Cite this article

Ilya Shapiro, Hopf-cyclic coefficients in the braided setting. J. Noncommut. Geom. 19 (2025), no. 3, pp. 971–1013

DOI 10.4171/JNCG/584