The sh-Lie algebra perturbation lemma
-
Johannes Huebschmann
Abstract
Let R be a commutative ring which contains the rationals as a subring and let g be a chain complex. Suppose given an sh-Lie algebra structure on g, that is, a coalgebra perturbation of the coalgebra differential on the cofree coaugmented differential graded cocommutative coalgebra T′ on the suspension of g and write the perturbed coalgebra as T″. Suppose, furthermore, given a contraction of g onto a chain complex M. We show that the data determine an sh-Lie algebra structure on M, that is, a coalgebra perturbation of the coalgebra differential on the cofree coaugmented differential graded cocommutative coalgebra S′ on the suspension of M, a Lie algebra twisting cochain from the perturbed coalgebra S″ to the loop Lie algebra L on the perturbed coalgebra T″, and an extension of this Lie algebra twisting cochain to a contraction of chain complexes from the Cartan–Chevalley–Eilenberg coalgebra on L onto S″ which is natural in the data. For the special case where M and g are connected we also construct an explicit extension of the perturbed retraction to an sh-Lie map. This approach includes a very general solution of the master equation.
© de Gruyter 2011
Artikel in diesem Heft
- The sh-Lie algebra perturbation lemma
- Gradient estimates in Orlicz spaces for nonlinear elliptic equations with BMO nonlinearity in nonsmooth domains
- Geography of non-formal symplectic and contact manifolds
- Hp → Hp boundedness implies Hp → Lp boundedness
- Global regularity for the minimal surface equation in Minkowskian geometry
- On elementarily κ-homogeneous unary structures
- Kernels, regularity and unipotent radicals in linear algebraic monoids
- Mod-Gaussian convergence: new limit theorems in probability and number theory
- Uniform large deviation for pinned hyperbolic Brownian motion
Artikel in diesem Heft
- The sh-Lie algebra perturbation lemma
- Gradient estimates in Orlicz spaces for nonlinear elliptic equations with BMO nonlinearity in nonsmooth domains
- Geography of non-formal symplectic and contact manifolds
- Hp → Hp boundedness implies Hp → Lp boundedness
- Global regularity for the minimal surface equation in Minkowskian geometry
- On elementarily κ-homogeneous unary structures
- Kernels, regularity and unipotent radicals in linear algebraic monoids
- Mod-Gaussian convergence: new limit theorems in probability and number theory
- Uniform large deviation for pinned hyperbolic Brownian motion
