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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Tensor product of Hopf bimodules over a group
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by Claude Cibils PDF
Proc. Amer. Math. Soc. 125 (1997), 1315-1321 Request permission

Abstract:

We describe the monoidal structure of the category of Hopf bimodules of a finite group and we derive a surjective ring map from the Grothendieck ring of the category of Hopf bimodules to the center of the integral group ring. We consider analogous results for the multiplicative structure of the Hochschild cohomology.
References
  • D. J. Benson, Representations and cohomology. I, Cambridge Studies in Advanced Mathematics, vol. 30, Cambridge University Press, Cambridge, 1991. Basic representation theory of finite groups and associative algebras. MR 1110581
  • Alain Bruguières, Théorie tannakienne non commutative, Comm. Algebra 22 (1994), no. 14, 5817–5860 (French, with English summary). MR 1298753, DOI 10.1080/00927879408825165
  • Saunders MacLane, Steinitz field towers for modular fields, Trans. Amer. Math. Soc. 46 (1939), 23–45. MR 17, DOI 10.1090/S0002-9947-1939-0000017-3
  • Cibils C., Rosso M.: Algèbres des chemins quantiques. Publication interne, Genève (1993) et prépublication de l’IRMA 047, Strasbourg (1993). To appear in Advances in Maths.
  • Cibils, C., Solotar, A.: Hochschild cohomology algebra and Hopf bimodules of an abelian group. Prepublication.
  • Charles W. Curtis and Irving Reiner, Methods of representation theory. Vol. I, Wiley Classics Library, John Wiley & Sons, Inc., New York, 1990. With applications to finite groups and orders; Reprint of the 1981 original; A Wiley-Interscience Publication. MR 1038525
  • P. Deligne, Catégories tannakiennes, The Grothendieck Festschrift, Vol. II, Progr. Math., vol. 87, Birkhäuser Boston, Boston, MA, 1990, pp. 111–195 (French). MR 1106898
  • R. Dijkgraaf, V. Pasquier, and P. Roche, Quasi Hopf algebras, group cohomology and orbifold models, Nuclear Phys. B Proc. Suppl. 18B (1990), 60–72 (1991). Recent advances in field theory (Annecy-le-Vieux, 1990). MR 1128130, DOI 10.1016/0920-5632(91)90123-V
  • V. G. Drinfel′d, Quantum groups, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Berkeley, Calif., 1986) Amer. Math. Soc., Providence, RI, 1987, pp. 798–820. MR 934283
  • Jones, V.: Fusion en algèbres de von Neumann et groupes de lacets [d’après A. Wassermann]. Séminaire Bourbaki 800 1995
  • Christian Kassel, Quantum groups, Graduate Texts in Mathematics, vol. 155, Springer-Verlag, New York, 1995. MR 1321145, DOI 10.1007/978-1-4612-0783-2
  • Luzstig, G. Leading coefficients of character values of Hecke algebras. Arcata Conference on Representations of Finite Groups. Proc. of Symp. in Pure Math. 47 A.M.S. 1987
  • Susan Montgomery, Hopf algebras and their actions on rings, CBMS Regional Conference Series in Mathematics, vol. 82, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 1993. MR 1243637, DOI 10.1090/cbms/082
  • Warren D. Nichols, Bialgebras of type one, Comm. Algebra 6 (1978), no. 15, 1521–1552. MR 506406, DOI 10.1080/00927877808822306
  • Zhong Qi Ma, Representations of the braid group obtained from quantum $\textrm {sl}(3)$ enveloping algebra, J. Math. Phys. 31 (1990), no. 3, 550–556. MR 1039204, DOI 10.1063/1.528888
  • Marc Rosso, Groupes quantiques et algèbres de battage quantiques, C. R. Acad. Sci. Paris Sér. I Math. 320 (1995), no. 2, 145–148 (French, with English and French summaries). MR 1320345
  • Wassermann, A.: Fusion for von Neumann algebras and loop groups, to appear.
  • S. L. Woronowicz, Differential calculus on compact matrix pseudogroups (quantum groups), Comm. Math. Phys. 122 (1989), no. 1, 125–170. MR 994499
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Additional Information
  • Claude Cibils
  • Affiliation: Mathematisches Institut, Universität Bern, Sidlerstrasse 5, CH-3012 Bern, Switzerland; Institut Fourier, Laboratoire de Mathématiques, URA 188 du CNRS, BP 74, F-38402 St. Martin d’Hères cedex, France
  • Address at time of publication: Départemente de Mathématiques, Université de Montpellier 2, F-34095 Montpellier cedex 5, France
  • MR Author ID: 49360
  • ORCID: 0000-0003-3269-9525
  • Email: cibils@math.univ-montp2.fr
  • Received by editor(s): July 27, 1995
  • Received by editor(s) in revised form: December 1, 1995
  • Additional Notes: Supported by University of Bern and University of Grenoble
  • Communicated by: Ken Goodearl
  • © Copyright 1997 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 125 (1997), 1315-1321
  • MSC (1991): Primary 18D10, 20G05, 20G10
  • DOI: https://doi.org/10.1090/S0002-9939-97-03727-1
  • MathSciNet review: 1371118