Non-Abelian Lie algebroids over jet spaces

DOI10.1080/14029251.2014.900992zbMath1420.37069arXiv1305.4598OpenAlexW3105889494MaRDI QIDQ5230943

Arthemy V. Kiselev, Andrey Krutov

Publication date: 29 August 2019

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

Full work available at URL: https://arxiv.org/abs/1305.4598

zbMATH Keywords

zero-curvature representationgauge transformationmaster equationLie algebroidhomological vector field

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Yang-Mills and other gauge theories in quantum field theory (81T13) Quantization in field theory; cohomological methods (81T70) Jets in global analysis (58A20) Poisson manifolds; Poisson groupoids and algebroids (53D17) Yang-Mills and other gauge theories in mechanics of particles and systems (70S15)

Related Items (4)

The calculus of multivectors on noncommutative jet spaces ⋮ On the (non)removability of spectral parameters in \(\mathbb{Z}_{2}\)-graded zero-curvature representations and its applications ⋮ The deformation quantisation mapping of Poisson to associative structures in field theory ⋮ Non-degenerate invariant (super)symmetric bilinear forms on simple Lie (super)algebras

Cites Work

• Unnamed Item
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• Derived brackets
• Hamiltonian flows on Euler-type equations
• Quantum inverse problem method. I
• Variational Poisson-Nijenhuis structures for partial differential equations
• Quantum field theory and the Jones polynomial
• Topological sigma models
• Integration of nonlinear equations of mathematical physics by the method of inverse scattering. II
• On symmetries and cohomological invariants of equations possessing flat representations
• On the horizontal gauge cohomology and nonremovability of the spectral parameter
• Remarks on two approaches to the horizontal cohomology: Compatibility complex and the Koszul--Tate resolution
• Deformation quantization of Poisson manifolds
• Symmetry algebras of Lagrangian Liouville-type systems
• The Geometry of the Master Equation and Topological Quantum Field Theory
• Involutive distributions of operator-valued evolutionary vector fields and their affine geometry. II
• Notes on A∞-Algebras, A∞-Categories and Non-Commutative Geometry
• Lie algebroids and homological vector fields
• A note on gauge systems from the point of view of Lie algebroids
• Horizontal cohomology with coefficients and non-linear zero-curvature representations
• A comparison of definitions for the Schouten bracket on jet spaces
• Quantum invariants of knots and 3-manifolds

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