Weak Hopf algebras corresponding to Cartan matrices

DOI10.1063/1.1933063zbMath1110.16047arXivmath/0504494OpenAlexW3098095903MaRDI QIDQ3438525

Shilin Yang

Publication date: 16 May 2007

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0504494

zbMATH Keywords

weak Hopf algebrassemisimple Lie algebrasquantized enveloping algebrasgrouplike elements

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)

Related Items (15)

The extension of a quantized Borcherds superalgebra by a Hopf algebra ⋮ Weak quantum Borcherds superalgebras and their representations ⋮ Construct weak Hopf algebras by using Borcherds matrix. ⋮ Extensions of quantum enveloping algebras ⋮ Weak Hopf algebras corresponding to quantum algebras \(U_q(f(K,H))\) ⋮ Double weak Hopf quiver and its path coalgebra ⋮ The equitable presentation for the weak quantum group \(\omega U_{Q}(\mathcal G)\) ⋮ Weak Hopf algebras corresponding to Borcherds-Cartan matrices. ⋮ Nichols algebras over weak Hopf algebras ⋮ Lusztig symmetries and Poincare-Birkhoff-Witt basis for $\mathfrak {wU}_{r, s}^{\mathrm{d}}({\rm osp}(1|2n))$wUr,sd( osp (1|2n)) ⋮ A class of weak Hopf algebras. ⋮ Some graded bialgebras related to Borcherds superalgebras ⋮ Green rings of weak Hopf algebras based on generalized Taft algebras ⋮ Singular Solutions to the Quantum Yang–Baxter Equations ⋮ Weak quantum enveloping algebras of Borcherds superalgebras

Cites Work

• Left Hopf algebras
• An algebra related to the fusion rules of Wess-Zumino-Witten models
• Real forms of \({\mathcal U}_ q({\mathfrak g})\)
• Weak Hopf algebras and some new solutions of the quantum Yang-Baxter equation
• Duality for generalized Kac algebras and a characterization of finite groupoid algebras
• Weak Hopf algebras. I: Integral theory and \(C^*\)-structure
• The Coradical Filtration for Quantized Enveloping Algebras
• Weak Hopf algebras corresponding to Uq[sln]
• The Coradical Filtration for Quantized Enveloping Algebras
• The coradical filtration ofU_q(g)at roots of unity
• Introduction to quantum groups
• Weak Hopf algebras and singular solutions of quantum Yang-Baxter equation

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