Finite Hopf algebras in braided tensor categories

DOI10.1016/S0022-4049(97)00207-7zbMath0936.16038MaRDI QIDQ1295759

Mitsuhiro Takeuchi

Publication date: 22 February 2000

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

zbMATH Keywords

antipodesintegralstensor productsbialgebrasHopf modulesbraided monoidal categoriesfinite Hopf algebras

Mathematics Subject Classification ID

Related Items

Factorizable quasi-Hopf algebras -- applications. ⋮ A quantum double construction in Rel ⋮ The relative modular object and Frobenius extensions of finite Hopf algebras ⋮ Hopf categories ⋮ A PARTIALLY DEFINED BRAIDING ON A NON-BRAIDED CATEGORY C ⋮ Braided module and comodule algebras, Galois extensions and elements of trace 1. ⋮ The antipode and the (co)invariants of a finite Hopf (co)quasigroup ⋮ Constructing non-semisimple modular categories with local modules ⋮ Duality for infinite-dimensional braided bialgebras and their (co)modules ⋮ \(\mathbb Z/2\mathbb Z\)-extensions of Hopf algebra module categories by their base categories ⋮ A Larson-Sweedler theorem for Hopf \(\mathcal{V} \)-categories ⋮ Unnamed Item ⋮ EXAMPLES OF POINTED COLOR HOPF ALGEBRAS ⋮ On finite dimensional Nichols algebras of diagonal type ⋮ THE NICHOLS ZOELLER THEOREM FOR HOPF ALGEBRAS IN THE CATEGORY OF YETTER DRINFELD MODULES ⋮ Braided Hopf algebras obtained from coquasitriangular Hopf algebras. ⋮ A sequence to compute the Brauer group of certain quasi-triangular Hopf algebras. ⋮ THE HOPF AUTOMORPHISM GROUP AND THE QUANTUM BRAUER GROUP IN BRAIDED MONOIDAL CATEGORIES ⋮ Universal deformation formulas and braided module algebras. ⋮ Unnamed Item ⋮ Non-degeneracy conditions for braided finite tensor categories ⋮ Hopf Algebras ⋮ Yetter-Drinfeld Categories for Quasi-Hopf Algebras ⋮ A Braided Version of Some Results of Skryabin ⋮ A Categorical Approach to Turaev's Hopf Group-Coalgebras ⋮ A freeness theorem for Nichols algebras ⋮ Hopf Semialgebras ⋮ Theory of braided Hopf crossed products

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Biinvertible actions of Hopf algebras
• The structure of Hopf algebras with a projection
• Quantum groups and quantum determinants
• Braided tensor categories
• Modular transformations for tensor categories
• Reconstruction of hidden symmetries
• On the structure of Hopf algebras
• Quantum group constructions in a symmetric monoidal category
• Quantum groups and representations of monoidal categories
• Generalized Lie algebras
• Two dual classes of bialgebras related to the concepts of “quantum group” and “quantum lie algebra”
• Hopf modules in yetter-drinfeld categories
• GAUSS CODES, QUANTUM GROUPS AND RIBBON HOPF ALGEBRAS
• Frobenius extensions of subalgebras of Hopf algebras
• An Associative Orthogonal Bilinear Form for Hopf Algebras