Omni-representations of Leibniz conformal algebras

@misc{benabdelhafidh2026omnirepresentations,
  title = {{Omni-representations of Leibniz conformal algebras}},
  author = {Sami Benabdelhafidh},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.33856},
  eprint = {2610.33856},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.33856},
}

TY  - UNPB
TI  - Omni-representations of Leibniz conformal algebras
AU  - Sami Benabdelhafidh
PY  - 2026
DA  - 2026/10/24
PB  - arXiv
DO  - 10.48550/arxiv.2610.33856
UR  - https://arxiv.org/abs/2610.33856
AB  - In this paper, we introduce the notion of an omni-representation of a Leibniz conformal algebra g on a ℂ[∂]-module M as a Leibniz conformal algebra homomorphism from g to the conformal omni-Lie algebra gc(M)⊕ M. We show that the right λ-action of a representation induces a Maurer--Cartan element. When M is a free ℂ[∂]-module of finite rank, it also defines, via the conformal dual M_c^*, a $1$-cocycle with values in M_c^*⊗ M≅gc(M). Consequently, every such representation gives rise to an omni-representation on M_c^*⊗ M. We characterize omni-representations with values in the graph of a conformal embedding tensor. Finally, we introduce the omni-cohomology theory of Leibniz conformal algebras and establish the relation between omni-cohomology groups and the usual cohomology groups.
ER  -