Representations of some Hopf algebras associated to the symmetric group \(S_n\).

DOI10.1007/s10468-008-9099-0zbMath1200.16048arXivmath/0701495OpenAlexW2593201050MaRDI QIDQ735227

Susan Montgomery, Andrea Jedwab

Publication date: 21 October 2009

Published in: Algebras and Representation Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0701495

zbMATH Keywords

symmetric groupssemisimple Hopf algebrassimple modulesDrinfeld doublesbismash productsFrobenius-Schur indicatorsexact factorizations

Mathematics Subject Classification ID

Representations of orders, lattices, algebras over commutative rings (16G30) Ordinary representations and characters (20C15) Symmetric groups (20B30) Products of subgroups of abstract finite groups (20D40) Smash products of general Hopf actions (16S40) Hopf algebras and their applications (16T05)

Related Items (11)

HIGHER INDICATORS FOR SOME GROUPS AND THEIR DOUBLES ⋮ Frobenius-Schur indicators for some fusion categories associated to symmetric and alternating groups ⋮ Aq-Identity Related to a Comodule ⋮ Finite quantum groups and quantum permutation groups. ⋮ An indicator formula for the Hopf algebra \(k^{S_{n-1}}\# kC_n\) ⋮ Some bismash products that are not group algebras. ⋮ On fusion rules and solvability of a fusion category ⋮ On the trace of the antipode and higher indicators. ⋮ Frobenius-Schur indicators for subgroups and the Drinfel’d double of Weyl groups ⋮ Indicators of bismash products from exact symmetric group factorizations ⋮ On the algebra structure of some bismash products.

Cites Work

• Central invariants and Frobenius-Schur indicators for semisimple quasi-Hopf algebras.
• Hopf powers and orders for some bismash products.
• Finite dimensional cosemisimple Hopf algebras in characteristic 0 are semisimple
• Realizability of representations of finite groups
• A construction of representations of Weyl groups
• Calculations of some groups of Hopf algebra extensions
• On group theoretical Hopf algebras and exact factorizations of finite groups.
• Computing the Frobenius-Schur indicator for Abelian extensions of Hopf algebras
• Self-dual modules of semisimple Hopf algebras.
• Some bismash products that are not group algebras.
• Frobenius-Schur indicators for a class of fusion categories.
• Frobenius-Schur indicators for subgroups and the Drinfel’d double of Weyl groups
• Semisimple Cosemisimple Hopf Algebras
• Matched pairs of groups and bismash products of hopf algebras
• S 4 symmetry of 6j symbols and Frobenius–Schur indicators in rigid monoidal C* categories
• On higher Frobenius-Schur indicators
• On Recursions Connected With Symmetric Groups I
• A Frobenius-Schur theorem for Hopf algebras
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