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- Title
Algebras of slowly growing length.
- Authors
Guterman, Alexander; Kudryavtsev, Dmitry
- Abstract
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.
- Subjects
ALGEBRA; ASSOCIATIVE algebras; LIE algebras; NONASSOCIATIVE algebras; POLYNOMIALS
- Publication
International Journal of Algebra & Computation, 2022, Vol 32, Issue 7, p1307
- ISSN
0218-1967
- Publication type
Article
- DOI
10.1142/S0218196722500564