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Ribbon Yetter–Drinfeld modules and tangle invariants

Kazuo Habiro

https://orcid.org/0000-0002-2263-3832

Department of Mathematics, Kyoto University, Kitashirakawa-Oiwakecho, Sakyo-ku, Kyoto 606-8502, Japan

E-mail Address: habiro@math.kyoto-u.ac.jp

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and

Yuka Kotorii

https://orcid.org/0000-0003-2192-5718

Mathematics Program, Graduate school of Advanced Science and Engineering, Hiroshima University, 1-7-1 Kagamiyama Higashi-Hiroshima City, Hiroshima 739-8521, Japan

International Institute for Sustainability with Knotted Chiral, Meta Matter (WPI-SKCM²), WPI Hiroshima University, 2-313 Kagamiyama Higashi-hiroshima City, Hiroshima 739-0046, Japan

Interdisciplinary Theoretical and, Mathematical Sciences Program, RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan

E-mail Address: kotorii@hiroshima-u.ac.jp

Corresponding author

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https://doi.org/10.1142/S179352532350019XCited by:0 (Source: Crossref)

Abstract

We define notions of pivotal and ribbon objects in a monoidal category. These constructions give pivotal or ribbon monoidal categories from a monoidal category which is not necessarily with duals. We apply this construction to the braided monoidal category of Yetter–Drinfeld modules over a Hopf algebra. This gives rise to the notion of ribbon Yetter–Drinfeld modules over a Hopf algebra, which form ribbon categories. This gives an invariant of tangles.

Keywords:

AMSC: 18M15, 16T05, 57K16, 57K10