From bosonized osp(1|2) to liftings of the super Jordan plane

@misc{lu2026from,
  title = {{From bosonized $\mathfrakosp(1|2)$ to liftings of the super Jordan plane}},
  author = {Tao Lu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.10098},
  eprint = {2610.10098},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.10098},
}

TY  - UNPB
TI  - From bosonized osp(1|2) to liftings of the super Jordan plane
AU  - Tao Lu
PY  - 2026
DA  - 2026/10/07
PB  - arXiv
DO  - 10.48550/arxiv.2610.10098
UR  - https://arxiv.org/abs/2610.10098
AB  - We study a family of liftings U(λ) of the super Jordan plane over the infinite cyclic group in characteristic zero. For a nonzero lifting parameter λ, we identify a natural subalgebra B with the bosonization of U(osp(1|2)), also known as sl_−1(2), and show that the lifting U(λ) is obtained from B by an Ore localization at a single distinguished element. This structural description provides a unified approach to the representation theory and ideal structure of U(λ). We classify the finite-dimensional simple modules of B and prove that every finite-dimensional B-module is completely reducible; the localization then yields the corresponding results for U(λ). We determine the prime, primitive, and completely prime ideals of both algebras. Finally, we compute their classical quotient rings, showing in particular that the classical quotient ring of U(λ) is a 2×2 matrix algebra over the skew field of fractions of the tensor product of its centre and the first Weyl algebra.
ER  -