2026/02/16 by Domenico Fiorenza, Antonio Michele Miti · 1 voice
Mathematics · Physics and Astronomy · #math.SG #math-ph #math.DG
In "Lie infinity algebras and higher analogues of Dirac structures and Courant algebroids" [arXiv:1003.1004], Marco Zambon constructs an L_∞-algebra associated with any higher standard or twisted Courant algebroid (also known as a Vinogradov algebroid), and exhibits an explicit L_∞-morphism from the Lie algebra associated with a standard Lie algebroid twisted by a closed 2-form to the Lie-2 algebra of the standard Courant algebroid. He poses the question of whether analogous canonical L_∞-morphisms exist in higher degrees -- namely, for any standard higher Courant algebroid twisted by a closed (r+1)-form. We adfirmatively answer this question, presenting a general framework that naturally yields such canonical L_∞-morphisms for arbitrary r, while at the same time clarifying the geometrical and homotopical structures underlying the construction. We also show how this framework accommodates the canonical morphism between Roger's observable L_∞-algebra of a pre-r-plectic manifold and the higher Courant algebra described by Zambon and one of the authors in "Observables on multisymplectic manifolds and higher Courant algebroids" [arXiv:2209.05836].