Alphabeta MathQuasi-Hopf, Weak Hopf, and Relative Tensor Products
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✓ 3 results · all verified · 1 also independently AI-judged
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1 · Prerequisites
Abstract Algebra
- Binary Operations, Monoids, Groups and Subgroups
- Chain Conditions, Semisimple Modules and the Wedderburn–Artin Theorem
- Cosets, Index and Lagrange's Theorem
- Free Modules, Exact Sequences, Projective and Injective Modules
- Group Homomorphisms and the Isomorphism Theorems
- Modules, Submodules, Quotient Modules and the Isomorphism Theorems
- Normal Subgroups and Quotient Groups
- Rings, Subrings, Integral Domains and Fields
- Tensor Products of Modules
Categorification and Geometric Representation Theory
Category Theory
Linear Algebra
Real Analysis
2 · Logical flowchart
3 · Items
Definition
Quasi-bialgebras, quasi-antipodes, and quasi-Hopf algebras
Definition
Weak bialgebras, weak Hopf algebras, and counital maps
Theorem
Modules over a quasi-bialgebra form a monoidal category
Lemma
Counital bases of a weak bialgebra
Remark
Quasi-Hopf and weak-Hopf extensions change different axioms
Proposition
Weak-bialgebra module tensor products are relative tensor products
Sources
- P. Etingof, S. Gelaki, D. Nikshych, and V. Ostrik, Tensor Categories
- F. Haußer and F. Nill, Doubles of Quasi-Quantum Groups
- P. Schauenburg, Weak Hopf Algebras and Quantum Groupoids
- G. Böhm and K. Szlachányi, Weak Hopf Algebras II: Representation Theory, Dimensions and the Markov Trace
- G. Böhm, S. Caenepeel, and K. Janssen, Weak Bialgebras and Monoidal Categories