Аннотация:
The search for a geometric interpretation of the constrained brackets of Dirac led to the definition of the Courant bracket. The search for the right notion of a “double” for Lie bialgebroids led to the definition of Courant algebroids. We recount the emergence of these concepts.
\RBibitem{Kos13}
\by Yvette~Kosmann-Schwarzbach
\paper Courant Algebroids. A Short History
\jour SIGMA
\yr 2013
\vol 9
\papernumber 014
\totalpages 8
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\crossref{https://doi.org/10.3842/SIGMA.2013.014}
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Эта публикация цитируется в следующих 17 статьяx:
Liu J., Sheng Yu., “Homotopy Poisson Algebras, Maurer-Cartan Elements and Dirac Structures of Clwx 2-Algebroids”, J. Noncommutative Geom., 15:1 (2021), 147–193
Gay-Balmaz F., Yoshimura H., “Dirac Structures in Nonequilibrium Thermodynamics For Simple Open Systems”, J. Math. Phys., 61:9 (2020), 092701
Lang H., Sheng Yu., “Linearization of the Higher Analogue of Courant Algebroids”, J. Geom. Mech., 12:4 (2020), 585–606
Jan Vysoký, “Hitchhiker's guide to Courant algebroid relations”, Journal of Geometry and Physics, 151 (2020), 103635
Vishnyakova E., “Graded Manifolds of Type and N-Fold Vector Bundles”, Lett. Math. Phys., 109:2 (2019), 243–293
Bruce A.J. Grabowski J., “Pre-Courant Algebroids”, J. Geom. Phys., 142 (2019), 254–273
Liu J., Sheng Yu., “Qp-Structures of Degree 3 and Clwx 2-Algebroids”, J. Symplectic Geom., 17:6 (2019), 1853–1891
M. J. Lean, “Dorfman connections and Courant algebroids”, J. Math. Pures Appl., 116 (2018), 1–39
M. J. Lean, C. Kirchhoff-Lukat, “Natural lifts of Dorfman brackets”, Adv. Theor. Math. Phys., 22:6 (2018), 1401–1446
Yunhe Sheng, “The First Pontryagin Class of a Quadratic Lie 2-Algebroid”, Commun. Math. Phys., 362:2 (2018), 689
B. Coueraud, “Dissections and automorphisms of regular Courant algebroids”, J. Geom. Phys., 119 (2017), 224–255
J. Liu, Yu. Sheng, Ch. Wang, “Omni n-Lie algebras and linearization of higher analogues of Courant algebroids”, Int. J. Geom. Methods Mod. Phys., 14:7 (2017), 1750113
Sheng Yu., Liu Zh., “From Leibniz Algebras To Lie 2-Algebras”, Algebr. Represent. Theory, 19:1 (2016), 1–5
Liu Zh., Sheng Yu., Xu X., “The Pontryagin class for pre-Courant algebroids”, J. Geom. Phys., 104 (2016), 148–162
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