A Hopf algebra associated to a Lie pair

Abstract

The quotient $L/A[-1]$ of a pair $A\hookrightarrow L$ of Lie algebroids is a Lie algebra object in the derived category $D^b(\mathcal{A})$ of the category $\mathcal{A}$ of left $\mathcal{U}(A)$-modules, the Atiyah class ${\alpha }_{L/A}$ being its Lie bracket. In this note, we describe the universal enveloping algebra of the Lie algebra object $L/A[-1]$ and we prove that it is a Hopf algebra object in $D^b(\mathcal{A})$.

6 pages

Cited by in corpus (4)

• Hochschild cohomology of dg manifolds associated to integrable distributions
• Hopf algebras arising from dg manifolds
• Atiyah classes of strongly homotopy Lie pairs
• Internal symmetry of the $L_{⩽3}$ algebra arising from a Lie pair