Smooth loops and loop bundles

DOI10.1016/j.aim.2021.108078zbMath1491.20155arXiv2008.08120OpenAlexW3211676494MaRDI QIDQ2054252

Sergey Grigorian

Publication date: 1 December 2021

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

Full work available at URL: https://arxiv.org/abs/2008.08120

zbMATH Keywords

holonomygauge theoryloopssmooth loopsChern-Simons functionalnon-associative

Mathematics Subject Classification ID

Loops, quasigroups (20N05) Issues of holonomy in differential geometry (53C29) Connections (general theory) (53C05)

Related Items

Nonassociative analogs of Lie groupoids, The Coulomb gauge in non-associative gauge theory

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Deformations of \(G_2\)-structures with torsion
• An octonionic formulation of the M-theory algebra
• Generalised Chern-Simons theory and \(G_{2}\)-instantons over associative fibrations
• \(G_{2}\)-structures and octonion bundles
• Bol loops as sections in semi-simple Lie groups of small dimension
• On the geometry of closed \(G_{2}\)-structures
• Curvature decomposition of \(G_2\)-manifolds
• Connections with \(L^ p \)bounds on curvature
• Lie groups and Lie algebras I. Foundations of Lie theory. Lie transformation groups. Transl. from the Russian by A. Kozlowski
• Local algebras of a multidimensional three-web
• Every Akivis algebra is linear
• Geometry of hyper-Kähler connections with torsion
• Theory of K-loops
• Free Akivis algebras, primitive elements, and hyperalgebras
• Riemannian geometry over different normed division algebras.
• Hyper-Kähler manifolds with torsion, supersymmetry and Hodge theory.
• \(G\)-loops and permutation groups
• An instanton-invariant for 3-manifolds
• Estimates and Monotonicity for a heat flow of isometric \(G_2\)-structures
• Über eine Beziehung zwischen Malcev-Algebren und Lie-Tripelsystemen
• The energy functional of \(G_2\)-structures compatible with a background metric
• A gradient flow of isometric \(\text{G}_2\)-structures
• Division Algebras and Supersymmetry I
• G₂-structures forN  =  1 supersymmetric AdS₄solutions ofM-theory
• Sur les groupes d'holonomie homogènes de variétés à connexion affine et des variétés riemanniennes
• Malcev Algebras
• Deformations of G₂ and Spin(7) Structures
• FLOWS OF G2-STRUCTURES, I
• Characteristic Classes. (AM-76)
• On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I
• The octonions
• A Bol Loop Isomorphic to all Loop Isotopes
• Bol Loops
• Loops in group theory and Lie theory