Home > Research > Publications & Outputs > Deformations and Homotopy Theory of Relative Ro...

Electronic data

  • Deformations_RB_revised-final-new

    Accepted author manuscript, 344 KB, PDF document

    Available under license: CC BY-NC: Creative Commons Attribution-NonCommercial 4.0 International License

Links

Text available via DOI:

View graph of relations

Deformations and Homotopy Theory of Relative Rota-Baxter Lie Algebras

Research output: Contribution to journalJournal articlepeer-review

Published
Close
<mark>Journal publication date</mark>15/04/2021
<mark>Journal</mark>Communications in Mathematical Physics
Volume383
Number of pages37
Pages (from-to)595–631
Publication StatusPublished
Early online date4/10/20
<mark>Original language</mark>English

Abstract

We determine the L∞-algebra that controls deformations of a relative Rota–Baxter Lie algebra and show that it is an extension of the dg Lie algebra controlling deformations of the underlying LieRep pair by the dg Lie algebra controlling deformations of the relative Rota–Baxter operator. Consequently, we define the cohomology of relative Rota–Baxter Lie algebras and relate it to their infinitesimal deformations. A large class of relative Rota–Baxter Lie algebras is obtained from triangular Lie bialgebras and we construct a map between the corresponding deformation complexes. Next, the notion of a homotopy relative Rota–Baxter Lie algebra is introduced. We show that a class of homotopy relative Rota–Baxter Lie algebras is intimately related to pre-Lie∞-algebras.

Bibliographic note

The final publication is available at Springer via https://doi.org/10.1007/s00220-020-03881-3