Frontiers of Mathematics in China >

2017 , Vol. 12 >Issue 1: 19 - 33

DOI: https://doi.org/10.1007/s11464-016-0590-3

RESEARCH ARTICLE

Weak rigid monoidal category

  • Haijun CAO
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  • School of Science, Shandong Jiaotong University, Jinan 250375, China

Received date: 30 Nov 2015

Accepted date: 07 Mar 2016

Published date: 01 Feb 2017

Copyright

2016 Higher Education Press and Springer-Verlag Berlin Heidelberg
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Abstract

We define the right regular dual of an object X in a monoidal category C , and give several results regarding the weak rigid monoidal category. Based on the definition of the right regular dual, we construct a weak Hopf algebra structure of H = End(F) whenever (F, J) is a fiber functor from category C to V ec and every X ∈ C has a right regular dual. To conclude, we give a weak reconstruction theorem for a kind of weak Hopf algebra.

Key words： Semilattice graded weak Hopf algebra; regular right dual; weak rigid monoidal category

Cite this article

Haijun CAO . Weak rigid monoidal category[J]. Frontiers of Mathematics in China, 2017 , 12(1) : 19 -33 . DOI: 10.1007/s11464-016-0590-3

References

Publishing order | Descend order by publishing year | Descend order by cited within
1
Cartier P. A primer of Hopf algebras. In: Cartier P, Julia B, Moussa P, Vanhove P, eds. Frontiers in Number Theory, Physics and Geometry II. Berlin: Springer, 2007, 537–615

DOI

2
Deligne P. Catégories tannakiennes. In: The Grothendieck Festschrift, Vol II. Progr Math, Vol 87. Basel: Birkhäuser, 1990, 111–196

3
Deligne P, Milne J. Tannakian categories. In: Lecture Notes in Math, Vol 900. Berlin: Springer, 1982, 101–228

4
Drinfield V. Quasi-Hopf algebras. Leningrad Math J, 1989, 1: 1419–1457

5
Etingof P, Schiffmann O. Lectures on Quantum Groups.Somerville: International Press, 1980

6
Hopf H. Über die Topologie der Gruppen-Mannigfaltigkeiten und ihrer Verallgemeinerungen. Ann of Math, 1941, 42: 22–52

DOI

7
Kelly G. On Mac Lane’s condition for coherence of natural associativities, commutativities, etc. J Algebra, 1964, 1: 397–402

DOI

8
Krein M. A principle of duality for a bicompact group and square block algebra. Dokl Akad Nauk SSSR, 1949, 69: 725–728

9
Li F. Weak Hopf algebras and some new solutions of quantum Yang-Baxter equation. J Algebra, 1998, 208: 72–100

DOI

10
Li F, Cao H J. Semilattice graded weak Hopf algebra and its related quantum G-double. J Math Phys, 2005, 46(8): 1–17

DOI

11
Mac Lane S. Natural associativity and commutativity. Rice Univ Studies, 1963, 49(4): 28–46

12
Mac Lane S. Categories for the working mathematician. 2nd ed. Grad Texts in Math, Vol 5. Berlin: Springer, 1998

13
Majid S. Foundations of Quantum Group Theory.Cambridge: Cambridge Univ Press, 2000

14
Saavedra Rivano N. Catégories Tannakiennes. Lecture Notes in Math, Vol 265. Berlin: Springer, 1972

15
Tannaka T. Über den Dualitätssatz der nichtkommutativen topologischen Gruppen. Tohoku Math J, 1939, 45: 1–12

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