Stable anti-Yetter-Drinfeld modules

By P. M. Hajac, Masoud Khalkhali, B. Rangipour, Yorck Sommerhaeuser. 2004

108 citations recorded by the source corpus.

We define and study a class of entwined modules (stable anti-Yetter–Drinfeld modules) that serve as coefficients for the Hopf-cyclic homology and cohomology. In particular, we explain their relationship with Yetter–Drinfeld modules and Drinfeld doubles. Among sources of examples of stable anti-Yetter–Drinfeld modules, we find Hopf–Galois extensions with a flipped version of the Miyashita–Ulbrich action. To cite this article: P.M. Hajac et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004).

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1b2d43edee4db9b9a6bdc81651ba7798560bc434

How researchers see this paper

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In Algebra and Number Theory

1. V. Ginzburg
2. Mihai D. Staic
3. Florin Panaite
4. I. Losev
5. A. Premet
6. T. Arakawa
7. Michel van den Bergh
8. Pavel Etingof

In Geometry and Topology

1. V. Ginzburg
2. Mihai D. Staic
3. Florin Panaite
4. I. Losev
5. I. Gordon
6. Michel van den Bergh
7. Pavel Etingof
8. T. Arakawa

In Mathematical Physics

1. V. Ginzburg
2. Mihai D. Staic
3. Florin Panaite
4. I. Losev
5. A. Premet
6. I. Gordon
7. Pavel Etingof
8. T. Arakawa

Citations in the corpus

• Lectures on Noncommutative Geometry (2005, background): “It is shown in [67] that modular pairs in involution are in fact one dimensional examples of stable anti-Yetter-Drinfeld modules over Hopf algebras introduced there.”
• Generalized (anti) Yetter-Drinfeld modules as components of a braided T-category (2005, methodology): “In particular, the category of anti-Yetter-Drinfeld modules coincides with H(S2,id)YD(H) H , which improves the remark in [7] that anti-Yetter-Drinfeld modules are entwined modules.”