On Frobenius algebras and the quantum Yang-Baxter equation

DOI10.1090/S0002-9947-97-01808-4zbMath0886.16019OpenAlexW1564747879MaRDI QIDQ4372569

Yuen Fong, Kostia I. Beidar, Alexander Stolin

Publication date: 16 December 1997

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-97-01808-4

zbMATH Keywords

symmetric algebrasAzumaya algebrasdual basesfinite-dimensional Lie algebrasFrobenius algebrasbraid relationsquantum Yang-Baxter equationstwist mapsFrobenius homomorphismsseparability idempotentsquasi-Frobenius Lie algebras

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Quasi-Frobenius rings (16L60)

Related Items (16)

Some remarks on Lie bialgebra structures on simple complex Lie algebras ⋮ Associative triples and the Yang-Baxter equation. ⋮ Hom-Yang-Baxter equations and Frobenius monoidal Hom-algebras ⋮ Rota-Baxter systems, dendriform algebras and covariant bialgebras ⋮ On antipodes and integrals in Hopf algebras over rings and the quantum Yang-Baxter equation ⋮ Nearly Frobenius dimension of Frobenius algebras ⋮ On Yang-Baxter equation and Calabi-Yau property of Koszul algebras ⋮ Infinite-dimensional Lie bialgebras via affinization of Novikov bialgebras and Koszul duality ⋮ On Frobenius algebras and the quantum Yang-Baxter equation ⋮ Hopf algebras and congruence subgroups ⋮ Konstantin Igorevich Beidar (1951-2004) ⋮ MORPHISMS OF DOUBLE FROBENIUS ALGEBRAS. II ⋮ On the classification of Lie bialgebras by cohomological means ⋮ Antipodes, preantipodes and Frobenius functors ⋮ FS-coalgebras and crossed coproducts ⋮ Modules, comodules, and cotensor products over Frobenius algebras

Cites Work

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• On rational solutions of Yang-Baxter equation for $\mathfrak{sl}(n)$.
• Constant solutions of Yang-Baxter equation for $\mathfrak{sl}(2)$ and $\mathfrak{sl}(3)$.
• QUASITRIANGULAR HOPF ALGEBRAS AND YANG-BAXTER EQUATIONS
• On Frobenius algebras and the quantum Yang-Baxter equation
• An Associative Orthogonal Bilinear Form for Hopf Algebras

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