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Identities on algebras and combinatorial properties of binary words
- Authors: Zacicev M.V.1,2, Repovs D.D.2
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Affiliations:
- Lomonosov Moscow State University
- University of Ljubljana
- Issue: Vol 489, No 5 (2019)
- Pages: 449-451
- Section: Mathematics
- URL: https://journals.eco-vector.com/0869-5652/article/view/18831
- DOI: https://doi.org/10.31857/S0869-56524895449-451
- ID: 18831
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Abstract
We consider polynomial identities and codimension growth of nonassociative algebras over a field of characte-ristics zero. We offer new approach which allows to construct nonassociative algebras starting from a given infinite binary word. The sequence of codimensions of such an algebra is closeely connected with combinatorial complexity of the defining word. These constructions give new examples of algebras with abnormal codimension growth. The first important achievement is that our algebras are finitely generated. The second one is that asymptotic behavior of codimension sequences is quite different unlike all previous examples.
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About the authors
M. V. Zacicev
Lomonosov Moscow State University; University of Ljubljana
Author for correspondence.
Email: zaicevmv@mail.ru
Russian Federation, 1, Leninskie gory, Moscow, 119991; 12, Kongresni trg, Ljubljana, Slovenia, 1000
D. D. Repovs
University of Ljubljana
Email: zaicevmv@mail.ru
Slovenia, 12, Kongresni trg, Ljubljana, 1000
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