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Licence: CC BY: Creative Commons Attribution 4.0 International License
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Deformations and Homotopy Theory of Relative Rota-Baxter Lie Algebras
AU - Lazarev, Andrey
AU - Sheng, Yunhe
AU - Tang, Rong
N1 - The final publication is available at Springer via https://doi.org/10.1007/s00220-020-03881-3
PY - 2021/4/15
Y1 - 2021/4/15
N2 - 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.
AB - 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.
U2 - 10.1007/s00220-020-03881-3
DO - 10.1007/s00220-020-03881-3
M3 - Journal article
VL - 383
SP - 595
EP - 631
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
SN - 0010-3616
ER -