Braided algebras and their applications to noncommutative geometry

DOI10.1016/j.aam.2013.02.004zbMath1292.17011arXiv1211.5506OpenAlexW1976356146MaRDI QIDQ394799

Dimitri Gurevich, Pavel A. Saponov

Publication date: 27 January 2014

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1211.5506

zbMATH Keywords

braidingSchwarzschild metricHecke symmetryLaplace-Betrami operatorquantum radiusreflection equation algebra

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Universal enveloping (super)algebras (17B35) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Noncommutative geometry (à la Connes) (58B34) Yang-Baxter equations (16T25)

Related Items (5)

Quantum geometry and quantization on \(U(u(2))\) background. Noncommutative Dirac monopole ⋮ Braided Rota–Baxter algebras, quantum quasi-shuffle algebras and braided dendriform algebras ⋮ Derivatives in noncommutative calculus and deformation property of quantum algebras ⋮ Drinfeld-Sokolov reduction in quantum algebras: canonical form of generating matrices ⋮ Generalizations of Poisson structures related to rational Gaudin model

Cites Work

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• Braided Weyl algebras and differential calculus on \(U(u(2))\)
• Braided differential operators on quantum algebras
• Spectral parameterization for power sums of a quantum supermatrix
• Quantum matrix algebras of the \(\text{GL}(m|n)\) type: the structure and spectral parameterization of the characteristic subalgebra
• Poincaré series of quantum spaces associated to Hecke operators
• Totally positive sequences and \(R\)-matrix quadratic algebras
• Differential calculus on compact matrix pseudogroups (quantum groups)
• Representation theory of (modified) reflection equation algebra of $GL(m|n)$ type
• Braided symmetric and exterior algebras
• On The Poincare Series of Quadratic Algebras Associated to Hecke Symmetries
• Covariant differential complexes on quantum linear groups
• Cayley–Hamilton theorem for quantum matrix algebras of $GL(m|n)$ type

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