REVIEW 1 cited by
Post-Lie deformations of pre-Lie algebras and their applications in Regularity Structures
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
read the original abstract
In this paper, we study post-Lie deformations of a pre-Lie algebra, namely deforming a pre-Lie algebra into a post-Lie algebra. We construct the differential graded Lie algebra that governs post-Lie deformations of a pre-Lie algebra. We also develop the post-Lie cohomology theory for a pre-Lie algebra, by which we classify infinitesimal post-Lie deformations of a pre-Lie algebra using the second cohomology group. The rigidity of such kind of deformations is also characterized using the second cohomology group. Finally, we apply this deformation theory to Regularity Structures. We prove that the post-Lie algebraic structure on the decorated trees which appears spontaneously in Regularity Structures is a post-Lie deformation of a pre-Lie algebra.
Forward citations
Cited by 1 Pith paper
-
An infinitesimal deformation of the post-Lie and post-Hopf algebra correspondence
Infinitesimal post-Lie/post-Hopf structures preserve the U⊣P adjunction and yield a Cartier–Milnor–Moore equivalence, with classifications on sl(2) and H4 and Koszulity of the IPL operad.
Discussion (0). Continue with ORCID to comment.