2025/12/03 by Ni, Dadi, Chen, Zhuo, Hu, Chuangqiang +1
#13D10 #16E45 #17B70 #53C05 #53C12 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA)
paper · doi:10.48550/arxiv.2512.03860
We study infinitesimal deformations of Lie algebroid pairs in the category of smooth manifolds enriched with a local Artinian algebra. Given a Lie algebroid pair (L,A), i.e. a Lie algebroid L together with a Lie subalgebroid A, we investigate isomorphism classes of infinitesimal deformations of (L,A) modulo automorphisms from exponentials of derivations of L and those from the exponentials of inner derivations of L, respectively. For the associated two deformation functors, we find the associated governing L_∞-algebras in the sense of extended deformation theory. Furthermore, when (L,A) is a matched Lie pair, i.e. the quotient L/A is also a Lie subalgebroid of L, we investigate isomorphism classes of infinitesimal deformations modulo automorphisms from exponentials of derivations along the normal direction L/A. The extended deformation theory of the associated deformation functor recovers the formal deformation theory of complex structures and that of transversely holomorphic foliations.