Mikhail Zaicev (Author), Dušan Repovš (Author)

Abstract

Numerical characteristics of polynomial identities of left nilpotent algebras are examined. Previously, we came up with a construction which, given an infinite binary word, allowed us to build a two-step left nilpotent algebra with specified properties of the codimension sequence. However, the class of the infinite words used was confined to periodic words and Sturm words. Here the previously proposed approach is generalized to a considerably more general case. I t is proved that fo r any algebra constructed given a binary word with subexponential function of combinatorial complexity, there exists a Pl-exponent. And its precise value is computed.

Keywords

left nilpotent algebra;polynomial identity;codimension;subexponential function of combinatorial complexity;PI-exponent;

Data

Year of publishing:
Typology: 1.01 - Original Scientific Article
Organization: UL FMF - Faculty of Mathematics and Physics
UDC: 512.557
COBISS: 18650201 Link will open in a new window
ISSN: 0373-9252
Views: 492
Downloads: 127
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Other data

Secondary language: English
Secondary title: Combinatorics on binary words and codimensions of identities in left nilpotent algebras
Secondary abstract: Numerical characteristics of polynomial identities of left nilpotent algebras are examined. Previously, we came up with a construction which, given an infinite binary word, allowed us to build a two-step left nilpotent algebra with specified properties of the codimension sequence. However, the class of the infinite words used was confined to periodic words and Sturm words. Here the previously proposed approach is generalized to a considerably more general case. I t is proved that fo r any algebra constructed given a binary word with subexponential function of combinatorial complexity, there exists a Pl-exponent. And its precise value is computed.
Secondary keywords: left nilpotent algebra;polynomial identity;codimension;subexponential function of combinatorial complexity;PI-exponent;
Type (COBISS): Article
Source comment: Angleški prevod v: ZAICEV, M., REPOVŠ, D. Combinatorics on binary words and codimensions of identities in left nilpotent algebras. Algebra and logic, ISSN 0002-5232, Volume 58, Number 1, March 2019, str. 23-35, DOI: 10.1007/s10469-019-09522-6, COBISS.SI-ID 18649945
Pages: str. 35-51
Volume: ǂT. ǂ58
Issue: ǂvyp. ǂ1
Chronology: 2019
ID: 11226237