Cohomologies and deformations of pre-Lie-morphism triples
Yibo Wang, Shilong Zhang, Jiefeng Liu
TL;DR
This paper develops cohomology theories for pre-Lie-morphism triples and explores their infinitesimal deformations, linking these to existing cohomology frameworks for Lie-morphism triples.
Contribution
It introduces a new cohomology for pre-Lie-morphism triples and connects it to the cohomology of Lie-morphism triples, advancing the understanding of their deformation theory.
Findings
Cohomology of pre-Lie-morphism triples is established.
Infinitesimal deformations are characterized via this cohomology.
A relation between pre-Lie and Lie cohomologies is demonstrated.
Abstract
A (pre-)Lie-morphism triple consists of two (pre-)Lie algebras and a (pre-)Lie algebra homomorphism between them. We give chomologies of pre-Lie-morphism triples. As an application, we study the infinitesimal deformations of pre-Lie-morphism triples. Finally, we show that the cohomology of the pre-Lie-morphism triple can be deduced from a new cohomology of the Lie-morphism triple.
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Taxonomy
TopicsAdvanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology · Ophthalmology and Eye Disorders