Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 31 min ago
PreprintarXiv licencearXiv

On the growth of Lie algebras and Jordan algebras

  • Be'eri Greenfeld
Open at sourcePDFDOICite

Abstract

We prove that every increasing, polynomially bounded function is realizable, up to bi-Lipschitz equivalence, as the growth function of some finitely generated Lie algebra. This does not extend to general increasing subexponential functions. We further prove that the classes of growth functions of Jordan algebras and associative algebras coincide, answering in the affirmative a question of Martínez and Zelmanov.

Related

  1. Structure of adjacency algebras of thin Jordan schemes
    Yudai Ohisa, Kyohei Yanagisawa
    arXivPreprintCC BY 4.0Full textCombinatorics & discrete mathematicsarXiv
  2. The Quasi-linearity problem for Jordan-Banach algebras: a topological characterization
    Gerardo M. Escolano
    arXivPreprintCC BY-NC-ND 4.0Full textAnalysis & PDEsarXiv
  3. Singular solutions from simple Euclidean Jordan algebras
    BaoZhi Chu
    arXivPreprintarXiv licenceFull textAlgebra & number theoryAnalysis & PDEsarXiv
  4. Non-abelian extensions of Hom-Jacobi-Jordan algebras
    Nejib Saadaoui
    arXivPreprintCC BY-NC-ND 4.0Full textAlgebra & number theoryarXiv
  5. Degenerations of Jordan algebras
    Victor Bovdi, Ivan Kaygorodov, Yury Popov +2
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{greenfeld2026growth,
  title = {{On the growth of Lie algebras and Jordan algebras}},
  author = {Be'eri Greenfeld},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.12852},
  eprint = {2609.12852},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.12852},
}
RIS
TY  - UNPB
TI  - On the growth of Lie algebras and Jordan algebras
AU  - Be'eri Greenfeld
PY  - 2026
DA  - 2026/09/11
PB  - arXiv
DO  - 10.48550/arxiv.2609.12852
UR  - https://arxiv.org/abs/2609.12852
AB  - We prove that every increasing, polynomially bounded function is realizable, up to bi-Lipschitz equivalence, as the growth function of some finitely generated Lie algebra. This does not extend to general increasing subexponential functions. We further prove that the classes of growth functions of Jordan algebras and associative algebras coincide, answering in the affirmative a question of Martínez and Zelmanov.
ER  -