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PreprintCC BY 4.0arXiv

Weak central polynomials for algebras of multiplications of simple algebras

  • Vesselin Drensky
  • Mikhail Zaicev
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Abstract

We give a simple proof for the existence of weak central polynomials for the algebra of multiplications of a finite-dimensional simple (non-associative) algebra. As an example we present explicit weak central polynomials in the cases of the three-dimensional simple Lie algebra and the Jordan algebra of the two-dimensional vector space with non-degenerate symmetric bilinear form.

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Cite

BibTeXRIS
BibTeX
@misc{drensky2026weak,
  title = {{Weak central polynomials for algebras of multiplications of simple algebras}},
  author = {Vesselin Drensky and Mikhail Zaicev},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.10362},
  eprint = {2609.10362},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.10362},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Weak central polynomials for algebras of multiplications of simple algebras
AU  - Vesselin Drensky
AU  - Mikhail Zaicev
PY  - 2026
DA  - 2026/09/09
PB  - arXiv
DO  - 10.48550/arxiv.2609.10362
UR  - https://arxiv.org/abs/2609.10362
AB  - We give a simple proof for the existence of weak central polynomials for the algebra of multiplications of a finite-dimensional simple (non-associative) algebra. As an example we present explicit weak central polynomials in the cases of the three-dimensional simple Lie algebra and the Jordan algebra of the two-dimensional vector space with non-degenerate symmetric bilinear form.
ER  -