Braided Weyl algebras and differential calculus on \(U(u(2))\)

DOI10.1016/j.geomphys.2011.12.002zbMath1259.17010arXiv1112.6258OpenAlexW2169271220WikidataQ115353239 ScholiaQ115353239MaRDI QIDQ413695

Dimitri Gurevich, Pavel Pyatov, Pavel A. Saponov

Publication date: 7 May 2012

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1112.6258

zbMATH Keywords

Laplace operatorpermutation relationsHecke symmetry(modified) reflection equation algebrabraided Weyl algebraradial part

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Noncommutative geometry (à la Connes) (58B34) Ring-theoretic aspects of quantum groups (16T20)

Related Items (9)

Generalized Heisenberg algebra, realizations of the \(\mathfrak{gl}(N)\) algebra and applications ⋮ Matrix Capelli identities related to reflection equation algebra ⋮ Braided algebras and their applications to noncommutative geometry ⋮ Quantum vector fields via quantum doubles and their applications ⋮ Quasi-derivations on 𝑈𝔤𝔩_{𝔫} and the argument shift method ⋮ Polygon gluing and commuting bosonic operators ⋮ Noncommutative geometry on central extension of U(u(2)) ⋮ The argument shift method in universal enveloping algebra \(U \mathfrak{gl}_d\) ⋮ Derivatives in noncommutative calculus and deformation property of quantum algebras

Cites Work

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• Quasideterminants. I
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• Representation theory of (modified) reflection equation algebra of $GL(m|n)$ type
• Braided affine geometry andq-analogs of wave operators
• On quantum matrix algebras satisfying the Cayley - Hamilton - Newton identities
• Covariant differential complexes on quantum linear groups
• Cayley–Hamilton theorem for quantum matrix algebras of $GL(m|n)$ type
• Covariant differential calculus on the quantum hyperplane

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