Welcome to Peter Schauenburg's homepage

Address

Institut de Mathématiques de Bourgogne - UMR 5584 CNRS
Université de Bourgogne
Faculté des Sciences Mirande
9 avenue Alain Savary
BP 47870 21078 Dijon Cedex
email: peter.schauenburg@u-bourgogne.fr

Most of my scientific papers

A Topological Invariant for Modular Fusion Categories (Joint with Ajinkya Kulkarni and Michaël Mignard)
Modular categories are not determined by their modular data (Joint with Michaël Mignard, Letters in Mathematical Physics volume 111, Article number: 60 (2021)
Higher Frobenius-Schur indicators for Drinfeld doubles of finite groups through characters of centralizers
Illustrating the algorithms in the paper, here are some indicator values:
- Indicators for the double of the symmetric group on 19 letters
- Indicators for the double of the symmetric group on 20 letters
- Indicators for the double of the symmetric group on 21 letters
- Indicators for the double of the symmetric group on 22 letters
- Indicators for the double of the symmetric group on 23 letters
- Indicators for the double of the symmetric group on 24 letters
- Indicators for the double of the symmetric group on 25 letters
A note on the restricted universal enveloping algebra of a restricted Lie-Rinehart Algebra ( Bull. Belg. Math. Soc. Simon Stevin 23 (2016), no. 5, 769–777)
The dual and the double of a Hopf algebroid are Hopf algebroids (Applied Categorical Structures 25 (2017), no. 1, 147–154)
Frobenius-Schur indicators for some fusion categories associated to symmetric and alternating groups ( Algebr. Represent. Theory 19 (2016), no. 3, 645–656)
A Higher Frobenius-Schur Indicator Formula for Group-Theoretical Fusion Categories (Communications in Mathematical Physics 340 (2015) 833-849;Erratum )
Some quasitensor autoequivalences of Drinfeld doubles of finite groups ( J. Noncommut. Geom. 11 (2017), no. 1, 51–70)
Computing Higher Frobenius-Schur Indicators in Fusion Categories Constructed from Inclusions of Finite Groups ( Pacific J. Math. 280 (2016), no. 1, 177–201)
On tensor factorizations of Hopf algebras (Joint with Marc Keilberg, Algebra Number Theory 10 (2016), no. 1, 61–87)
Module Categories of Finite Hopf Algebroids, and Self-Duality (Trans. Amer. Math. Soc. 369 (2017), no. 2, 1127–1146.)
Cohomology of finite dimensional pointed Hopf algebras (Joint with Mitja Mastnak, Julia Pevtsova, and Sarah Witherspoon, Proceedings of the London Mathematical Society 100 (2010) 377-404)
Congruence Subgroups and Generalized Frobenius-Schur Indicators (Joint with Siu-Hung Ng, Communications in Mathematical Physics, 300 (2010), no. 1, 1--46)
Frobenius-Schur indicators and exponents of spherical categories (Joint with Siu-Hung Ng, Advances in Mathematics 211 (2007), Issue 1, 34-71)
Central Invariants and Higher Indicators for Semisimple Quasi-Hopf Algebras (Joint with Siu-Hung Ng, Trans. Amer. Math. Soc. 360 (2008), 1839-1860)
Higher Frobenius-Schur Indicators for Pivotal Categories (Joint with Siu-Hung Ng, Contemporary Mathematics 441 (2007), 63-90)
Braided bi-Galois theory (Annali dell'Universitá di Ferrara - Sez. VII - Sc. Mat., Vol. LI (2005) 119-149)
Hopf Powers and Orders for Some Bismash Products (Joint with Rachel Landers and Susan Montgomery, Journal of Pure and Applied Algebra 205 (2006) Issue 1, 156-188)
On generalized Hopf Galois extensions (Joint with H.-J. Schneider, Journal of Pure and Applied Algebra 202 (2005) 168-194)
On the Frobenius-Schur indicators for quasi-Hopf algebras (Journal of Algebra 282 (2004) 129-139)
Two characterizations of finite quasi-Hopf algebras (Journal of Algebra 273 (2004) 538-550)
Hopf-Galois and bi-Galois extensions (in: Galois theory, Hopf algebras, and semiabelian categories, Fields Inst. Commun. 43, AMS 2004, pp. 469-515)
Quotients of finite-dimensional quasi-Hopf algebras (in: Hopf algebras in noncommutative geometry and physics, Dekker 2005, pp. 281-290)
Morita base change in quantum groupoids (in: Locally compact quantum groups and groupoids (Strasbourg, 2002), 79-103, IRMA Lecture Notes in Mathematics and Theoretical Physics 2, de Gruyter, Berlin, 2003)
Weak Hopf algebras and quantum groupoids (in: Noncommutative geometry and quantum groups (Warsaw, 2001), 171-188, Polish Acad. Sci., Warsaw, 2003)
A quasi-Hopf algebra freeness theorem (Proc. Amer. Math. Soc. 132 (2004) 965-972)
Turning monoidal categories into strict ones, ( New York Journal of Mathematics 7 (2001) 257-265)
Actions of monoidal categories, and generalized Hopf smash products (Journal of Algebra 270 (2003) 521-563)
Hopf modules and the double of a quasi-Hopf algebra ( Trans. Amer. Math. Soc. 354 (2002) 3349-3378)
Hopf algebra extensions and monoidal categories (in: New directions in Hopf algebras, Cambridge Univ. Press 2002, pp. 321-381)
Cohomological obstructions to cleft extensions over cocommutative Hopf algebras (K-Theory 24 (2001) 227-242)
Doi-Koppinen Hopf modules versus entwined modules, ( New York Journal of Mathematics 6 (2000) 325-330)
Duals and doubles of quantum groupoids (x_R-Hopf algebras), (In: "New trends in Hopf algebra theory", Proceedings of the colloquium on quantum groups and Hopf algebras, La Falda, Sierras de Cordoba, Argentina, August 1999, AMS Contemporary Mathematics 267 (2000) 273-299)
Hopf bimodules, coquasibialgebras, and an exact sequence of Kac, (Habilitationsschrift, '99, revised in Advances in Mathematics 165 (2002) 194-263)
The monoidal center construction and bimodules, (J. Pure Appl. Algebra 158 (2001) 325-346)
The structure of Hopf algebras with a weak projection, (Algebras and Representation Theory 3 (1999), 187-211)
A generalization of Hopf crossed products, (Communications in Algebra 27 (1999), 4779-4801)
Faithful flatness over Hopf subalgebras - counterexamples, (In: "Interactions between ring theory and representations of algebras", Proceedings of the conference held in Murcia, Spain, F. van Oystaeyen and M. Saorin, eds., Marcel Dekker 2000, pp. 331-344)
On the braiding on a Hopf algebra in a braided category, ( New York Journal of Mathematics 4 (1998) 259-263)
Galois objects over generalized Drinfeld doubles with an application to u_q(sl_2), (Journal of Algebra 217 (1999), 584-598)
Bigalois objects over the Taft algebras, (Israel J. Math. 115 (2000), 101-123)
Face algebras are x_R-bialgebras, (In: Rings, Hopf algebras, and Brauer groups, S. Caenepeel and A. Verschoren, eds., volume 197 of Lecture notes in pure and applied mathematics, Marcel Dekker, 1998)
Bialgebras over noncommutative rings and a structure theorem for Hopf bimodules, (Applied Categorical Structures 6 (1998) 193-222)
Examples of equivalences of Doi-Koppinen Hopf module categories, including Yetter-Drinfeld modules, (Bull. Belg. Math. Soc. 6 (1999), 91-98)
Galois correspondences for Hopf Bigalois extensions, (Journal of Algebra 201 (1998) 53-70)
Hopf Bigalois extensions, (Comm. in Algebra 24 (1996) 3797-3825)
A bialgebra that admits a Hopf-Galois extension is a Hopf algebra ( Proc. Amer. Math. Soc. 125 (1997), 83-85)
Hopf bimodules over Hopf-Galois extensions, Miyashita-Ulbrich actions, and monoidal center constructions, (Comm. in Algebra 24 (1996) 143-163)
Differential-Graded Hopf Algebras and Quantum Group Differential Calculi, (Journal of Algebra Volume 180, Issue 1, 15 February 1996, Pages 239–286)
Hopf Modules and Yetter - Drinfel′d Modules, (Journal of Algebra Volume 169, Issue 3, 1 November 1994, Pages 874–890)
On coquasitriangular Hopf algebras and the quantum Yang-Baxter equation, (Algebra Berichte 67 (1992), Verlag Reinhard Fischer, München)
Tannaka duality for arbitrary Hopf algebras, (Algebra Berichte 66 (1992), Verlag Reinhard Fischer, München)

Workshop on Fusion Categories, IMB Dijon 2013