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Prime ideals and representations of the bosonization of the super Jordan plane
Abstract
We study the Hopf algebra A given by the bosonization of the super Jordan plane over a field of characteristic not 2. We determine its centre, classical quotient ring, prime and primitive ideals. Over an algebraically closed base field, we classify all simple A-modules. In characteristic zero, simple modules are either finite-dimensional, of dimension 1 or 2, or infinite-dimensional, arising from a localization of the first Weyl algebra. Over an algebraically closed field of characteristic p>2, every simple module is finite-dimensional, of dimension 1, 2, or 2p, and we give explicit representatives for all isomorphism classes. Our approach relies on realizing a suitable localization of A as a matrix algebra.
Related
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BibTeX
@misc{lu2026prime,
title = {{Prime ideals and representations of the bosonization of the super Jordan plane}},
author = {Tao Lu},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.31012},
eprint = {2608.31012},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.31012},
}
RIS
TY - UNPB
TI - Prime ideals and representations of the bosonization of the super Jordan plane
AU - Tao Lu
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.31012
UR - https://arxiv.org/abs/2608.31012
AB - We study the Hopf algebra A given by the bosonization of the super Jordan plane over a field of characteristic not 2. We determine its centre, classical quotient ring, prime and primitive ideals. Over an algebraically closed base field, we classify all simple A-modules. In characteristic zero, simple modules are either finite-dimensional, of dimension 1 or 2, or infinite-dimensional, arising from a localization of the first Weyl algebra. Over an algebraically closed field of characteristic p>2, every simple module is finite-dimensional, of dimension 1, 2, or 2p, and we give explicit representatives for all isomorphism classes. Our approach relies on realizing a suitable localization of A as a matrix algebra.
ER -