Algebras of slowly growing length

Alexander Guterman, Dmitry Kudryavtsev

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We investigate the class of finite-dimensional not necessarily associative algebras that have slowly growing length, that is, for any algebra in this class its length is less than or equal to its dimension. We show that this class is considerably big, in particular, finite-dimensional Lie algebras as well as many other important classical finite-dimensional algebras belong to this class, for example, Leibniz algebras, Novikov algebras and Zinbiel algebras. The exact upper bounds for the length of these algebras is proved. To do this, we transfer the method of characteristic sequences to non-unital algebras and find certain polynomial conditions on the algebra elements that guarantee the slow growth of the length function.

Original languageEnglish
Pages (from-to)1307-1325
Number of pages19
JournalInternational Journal of Algebra and Computation
Issue number7
StatePublished - 1 Nov 2022
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2022 World Scientific Publishing Company.


  • Length of algebras
  • Lie algebras
  • non-associative algebras


Dive into the research topics of 'Algebras of slowly growing length'. Together they form a unique fingerprint.

Cite this