Toždestva v algebrah i kombinatornye svojstva dvoičnyh slov

Mikhail Zaicev (Author), Dušan Repovš (Author)

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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Data

Year of publishing:	2019
Typology:	1.03 - Short Scientific Article
Organization:	UL FMF - Faculty of Mathematics and Physics
UDC:	512.557
COBISS:	18867801
ISSN:	0869-5652
Views:	474
Downloads:	159
Average score:	0 (0 votes)
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Other data

Secondary language:	English
Secondary title:	Identities on algebras and combinatorial properties of binary words
Secondary 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.
Secondary keywords:	identities;codimensions;binary words;combinatorial complexity;
Type (COBISS):	Article
Source comment:	Angleški prevod v: ZAICEV, Mikhail, REPOVŠ, Dušan. Identities on algebras and combinatorial properties of binary words. Doklady, Mathematics, ISSN 1064-5624, 2019, vol. 100, no. 3, str. 558-559. https://doi.org/10.1134/S106456241906019X, doi: 10.1134/S106456241906019X. [COBISS.SI-ID 18945625]
Pages:	str. 449-451
Volume:	ǂT. ǂ489
Issue:	ǂno. ǂ5
Chronology:	2019
DOI:	10.31857/S0869-56524895449-451
ID:	11779594