On higher Frobenius-Schur indicators

By Yevgenia Kashina, Yorck Sommerhaeuser, Yongchang Zhu. 2003

131 citations recorded by the source corpus.

Introduction The calculus of Sweedler powers Frobenius-Schur indicators The exponent The order The index The Drinfel'd double Examples Bibliography Subject index Symbol index.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/32c68f0f779d23e355ee4607ea5ee5bf06edf8c1

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

In Discrete Mathematics and Combinatorics

In Geometry and Topology

Citations in the corpus

HOPF MONOIDS IN THE CATEGORY OF SPECIES (2012, background): “In the recent Hopf algebra literature, the operations h 7→ h are called Hopf powers [46] or Sweedler powers [36, 37].”
On fusion categories (2002, unknown): “h respect to the usual scalar product deﬁned by (bi,b∗ j) = δij) and hence invertible. The Lemma is proved. Remark 8.50. In the special case C = Rep(H) for some Hopf algebra HLemma 8.49 was proved in [KSZ] 6.3. Theorem 8.51. Let C be a fusion category over C and let Lbe an irreducible representation”
On the Frobenius–Schur indicators for quasi-Hopf algebras (2003, unknown): “Q A ] 7 S ep 2”
Higher Frobenius-Schur indicators for pivotal categories (2005, background): “In particular, the possible values of the higher Frobenius-Schur indicators are cyclotomic integers; this is well-known for the group case, where the higher indicators are in fact always integers, and proved for the Hopf algebra case in [9].”
Tensor categories: a selective guided tour (2008, methodology): “r(π: SL(2,Z) → GL(|I|,C)) ⊃ Γ(N) = ker(SL(2,Z) → SL(2,Z/NZ)). Proof announced by Ng/Schauenburg, using a categorical version [176] of the higher Frobenius-Schur indicators for Hopf algebras deﬁned in [110] and adapting the strategy of proof in [206]. 2. A modular category M gives rise to a surgery T”