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- W3213440130 abstract "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 $mathbb{N} Q$ manifolds and Voronov's higher derived brackets, each Dirac--Jacobi structure is associated with a cubic $L_infty$ algebra for any choice of a complementary almost Dirac--Jacobi structure. This $L_infty$ algebra governs the deformations of the Dirac--Jacobi structure: there is a one-to-one correspondence between the MC elements of this $L_infty$ algebra and the small deformations of the Dirac-Jacobi structure. Further, by Cattaneo and Schatz's equivalence of higher derived brackets, this $L_infty$ algebra does not depend (up to $L_infty$-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 $L_infty$ algebra of Dirac structure from the choice of a complementary almost Dirac structure (a result proved using other techniques by Gualtieri, Matviichuk and Scott)." @default.
- W3213440130 created "2021-11-22" @default.
- W3213440130 creator A5042318464 @default.
- W3213440130 date "2021-11-15" @default.
- W3213440130 modified "2023-09-27" @default.
- W3213440130 title "The Deformation $L_infty$ algebra of a Dirac--Jacobi structure." @default.
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