Skip to content
DraconiticResearch
Search Sources API
182,460 studies31 sourcesUpdated 37 min ago
PreprintCC BY-NC-ND 4.0arXiv

Extended π’ͺ-operators on Lie-Yamaguti Algebras

  • Wen Teng
Open at sourcePDFDOICite

Abstract

We study balanced extended π’ͺ-operators on Lie--Yamaguti algebras. The construction links operator equations, algebra splittings and Yang--Baxter equations. We build a double from a representation and a balanced equivariant map. The graphs of extended π’ͺ-operators are exactly its subalgebras complementary to the first summand. We define extended post-Lie--Yamaguti algebras and prove their two-way relation with extended π’ͺ-operators. The tensor form gives a balanced extended Lie--Yamaguti Yang--Baxter equation. We construct a curved L∞[1]-algebra whose Maurer--Cartan elements are extended π’ͺ-operators. The normal representation of a graph gives a cohomology theory for infinitesimal deformations, rigidity and obstructions. We include both cyclic conditions in the lowest paired degree. We also map operator infinitesimals to the deformation cohomology of the induced algebra. Examples give obstructed infinitesimals, rigid scalar operators and nontrivial formal deformations.

Related

  1. 1/2 derivations and biderivations of 3-dimensional nilpotent Lie-Yamaguti algebras
    Hassan Oubba
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  2. Rigid dualizing complex for quantum enveloping algebras and algebras of generalized differential operators
    Sophie Chemla
    Journal of AlgebraPeer-reviewedLicence not stated25 citedGeometry & topologyHAL
  3. Deformations and the controlling L∞-structure of extended Rota-Baxter Lie algebras
    Jian Yang
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  4. Einstein manifolds and extended PoincarΓ© algebras
    D. V. Alekseevsky, A. N. Lavrov
    arXivPreprintarXiv licenceFull textGeometry & topologyarXiv
  5. Deformation theory and the controlling L∞-structure of extended Rota-Baxter algebras
    Jian Yang
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{teng2026extended,
  title = {{Extended $\mathcalO$-operators on Lie-Yamaguti Algebras}},
  author = {Wen Teng},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.40686},
  eprint = {2610.40686},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.40686},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Extended π’ͺ-operators on Lie-Yamaguti Algebras
AU  - Wen Teng
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2610.40686
UR  - https://arxiv.org/abs/2610.40686
AB  - We study balanced extended π’ͺ-operators on Lie--Yamaguti algebras. The construction links operator equations, algebra splittings and Yang--Baxter equations. We build a double from a representation and a balanced equivariant map. The graphs of extended π’ͺ-operators are exactly its subalgebras complementary to the first summand. We define extended post-Lie--Yamaguti algebras and prove their two-way relation with extended π’ͺ-operators. The tensor form gives a balanced extended Lie--Yamaguti Yang--Baxter equation. We construct a curved L_∞[1]-algebra whose Maurer--Cartan elements are extended π’ͺ-operators. The normal representation of a graph gives a cohomology theory for infinitesimal deformations, rigidity and obstructions. We include both cyclic conditions in the lowest paired degree. We also map operator infinitesimals to the deformation cohomology of the induced algebra. Examples give obstructed infinitesimals, rigid scalar operators and nontrivial formal deformations.
ER  -