Classification of Finite-Dimensional Simple Novikov Algebras and Their Irreducible Bimodules in Positive Characteristic

We give a complete classification of finite-dimensional simple Novikov algebras over an algebraically closed field of characteristic $p>2$, including families missing from earlier classifications in \cite{Osborn1992, Xu1996}. We determine explicit normal forms and all isomorphisms between them, and classify all nontrivial irreducible bimodules over these algebras.

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-10-26
DOI
https://doi.org/10.48550/arxiv.2610.34896
Primary Topic
Advanced Topics in Algebra
Type
preprint
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preprint

Classification of Finite-Dimensional Simple Novikov Algebras and Their Irreducible Bimodules in Positive Characteristic

Yufeng Pei, Limeng Xia, Dong E. Liu
arXiv (Cornell University)
Advanced Topics in Algebra
preprint

Classification of Finite-Dimensional Simple Novikov Algebras and Their Irreducible Bimodules in Positive Characteristic

Yufeng Pei, Limeng Xia, Dong E. Liu
preprint en

Abstract

We give a complete classification of finite-dimensional simple Novikov algebras over an algebraically closed field of characteristic $p>2$, including families missing from earlier classifications in \cite{Osborn1992, Xu1996}. We determine explicit normal forms and all isomorphisms between them, and classify all nontrivial irreducible bimodules over these algebras.

arXiv (Cornell University)
Advanced Topics in Algebra
DOIOpen Access PDFOpenAlex
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Classification of Finite-Dimensional Simple Novikov Algebras and Their Irreducible Bimodules in Positive Characteristic — Yufeng Pei, Limeng Xia, et al. · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS