A construction of symmetric linear functions on the restricted quantum group \(\overline U_q(sl_2)\).

zbMath1201.16030arXiv0807.0052MaRDI QIDQ987173

Yusuke Arike

Publication date: 13 August 2010

Published in: Osaka Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0807.0052

zbMATH Keywords

primitive idempotentsrestricted quantum groupssymmetric linear functionsright integrals

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Quantum groups (quantized enveloping algebras) and related deformations (17B37) Vertex operators; vertex operator algebras and related structures (17B69) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Ring-theoretic aspects of quantum groups (16T20)

Related Items (12)

Non-semisimple 3-manifold invariants derived from the Kauffman bracket ⋮ Diagrammatic construction of representations of small quantum \(\mathfrak{sl}_2\) ⋮ Projective representations of mapping class groups in combinatorial quantization ⋮ Diagrammatic morphisms between indecomposable modules of Ūq(𝔰𝔩2) ⋮ Logarithmic Hennings invariants for restricted quantum \(\mathfrak{s}\mathfrak{l}\)(2) ⋮ A Heisenberg double addition to the logarithmic Kazhdan-Lusztig duality. ⋮ Quantum \(sl(2)\) action on a divided-power quantum plane at even roots of unity ⋮ Non-semisimple planar algebras from the representation theory of Ūq(𝔰𝔩2) ⋮ Representations of U¯qsℓ(2|1) at even roots of unity ⋮ Further results on the structure of (co)ends in finite tensor categories ⋮ A note on symmetric linear forms and traces on the restricted quantum group \(\bar U_q(\mathfrak{sl}(2))\) ⋮ Modular group representations in combinatorial quantization with non-semisimple Hopf algebras

Cites Work

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• Modular invariance of vertex operator algebras satisfying \(C_2\)-cofiniteness
• Modular group representations and fusion in logarithmic conformal field theories and in the quantum group center
• Kazhdan-Lusztig correspondence for the representation category of the triplet \(W\)-algebra in logarithmic CFT
• Quantum deformations of certain simple modules over enveloping algebras
• The trace function and Hopf algebras
• Modules over \(\mathfrak U_ q(\mathfrak s\mathfrak l_ 2)\)
• Conformal field theories associated to regular chiral vertex operator algebras. I: Theories over the projective line
• Modular invariance of characters of vertex operator algebras

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