Hopf algebras with trace and representations

DOI10.1007/s00222-004-0405-0zbMath1132.17007arXivmath/0304313OpenAlexW2008981239MaRDI QIDQ2484069

Marc Rosso, Nicolai Reshetikhin, Corrado De Concini, Claudio Procesi

Publication date: 2 August 2005

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0304313

zbMATH Keywords

irreducible representationquantized universal enveloping algebraClebsch-Gordan formulaCayley-Hamilton algebra

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37)

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Cites Work

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• Quantum Weyl group and a multiplicative formula for the R-matrix of a simple Lie algebra
• A formal inverse to the Cayley-Hamilton theorem
• Finite dimensional representations of algebras
• The invariant theory of \(n\times n\) matrices
• Azumaya algebras and Artin's theorem
• Some remarkable degenerations of quantum groups
• Quantum function algebra at roots of 1
• Regular elements of semisimple algebraic groups
• On Azumaya algebras and finite dimensional representations of rings
• Semisimple Representations of Quivers
• Quantum Coadjoint Action
• TRACE IDENTITIES OF FULL MATRIX ALGEBRAS OVER A FIELD OF CHARACTERISTIC ZERO