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PreprintCC BY 4.0arXiv

Right representations of Novikov algebras

  • A. S. Panasenko
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Abstract

We study the theory of right representations of Novikov algebras. We introduce the notion of a modular right ideal of a Novikov algebra and prove that every irreducible right representation of a Novikov algebra is isomorphic to the quotient by a maximal modular right ideal. We prove that the class of Novikov algebras with no irreducible representations forms a hereditary radical. We introduce the notion of a primitive Novikov algebra and show that a Novikov algebra is primitive if and only if it admits an almost faithful irreducible representation. We also introduce the notion of the quasi-kernel of a representation, defined as the largest ideal contained in its kernel. Finally, we prove that the constructed radical coincides with the intersection of the quasi-kernels of all its irreducible representations.

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Cite

BibTeXRIS
BibTeX
@misc{panasenko2026right,
  title = {{Right representations of Novikov algebras}},
  author = {A. S. Panasenko},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2606.16431},
  eprint = {2606.16431},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.16431},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Right representations of Novikov algebras
AU  - A. S. Panasenko
PY  - 2026
DA  - 2026/10/09
PB  - arXiv
DO  - 10.48550/arxiv.2606.16431
UR  - https://arxiv.org/abs/2606.16431
AB  - We study the theory of right representations of Novikov algebras. We introduce the notion of a modular right ideal of a Novikov algebra and prove that every irreducible right representation of a Novikov algebra is isomorphic to the quotient by a maximal modular right ideal. We prove that the class of Novikov algebras with no irreducible representations forms a hereditary radical. We introduce the notion of a primitive Novikov algebra and show that a Novikov algebra is primitive if and only if it admits an almost faithful irreducible representation. We also introduce the notion of the quasi-kernel of a representation, defined as the largest ideal contained in its kernel. Finally, we prove that the constructed radical coincides with the intersection of the quasi-kernels of all its irreducible representations.
ER  -