2021/11/14 by Alfonso Giuseppe Tortorella, Tortorella, Alfonso Giuseppe
Mathematics · Physics and Astronomy · #17B63 #17B70 #53D10 #53D17 #58A50 #58H15 #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2111.07467
openalex publication_date 2021/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We develop the deformations theory of a Dirac--Jacobi structure within a fixed Courant--Jacobi algebroid. Using the description of split Courant--Jacobi algebroids as degree 2 contact ℕ Q manifolds and Voronov's higher derived brackets, each Dirac--Jacobi structure is associated with a cubic L_∞ algebra for any choice of a complementary almost Dirac--Jacobi structure. This L_∞ algebra governs the deformations of the Dirac--Jacobi structure: there is a one-to-one correspondence between the MC elements of this L_∞ algebra and the small deformations of the Dirac-Jacobi structure. Further, by Cattaneo and Schätz's equivalence of higher derived brackets, this L_∞ algebra does not depend (up to L_∞-isomorphisms) on the choice of the complementary almost Dirac--Jacobi structure. These same ideas apply to get a new proof of the independence of the L_∞ algebra of Dirac structure from the choice of a complementary almost Dirac structure (a result proved using other techniques by Gualtieri, Matviichuk and Scott).