$\mathbb{Z}_2$-graded codimensions of unital algebras

Repovš, Dušan (author), Zaicev, Mikhail (author)

We study polynomial identities of nonassociative algebras constructed by using infinite binary words and their combinatorial properties. Infinite periodic and Sturmian words were first applied for constructing examples of algebras with an arbitrary real PI-exponent greater than one. Later, we used these algebras for a confirmation of the conjecture that PI-exponent increases precisely by one after adjoining an external unit to a given algebra. Here, we prove the same result for these algebras for graded identities and graded PI-exponent, provided that the grading group is cyclic of order two.

• Language: English
• Keywords: polynomial identities, graded algebras, codimensions, exponential growth
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education; FMF - Faculty of Mathematics and Physics
• Year: 2018
• Number of pages: Str. 483-500
• Numbering: Vol. 28, no. 3
• PID: 20.500.12556/RUL-109453
• UDC: 512.554
• ISSN on article: 0218-1967
• DOI: 10.1142/S0218196718500224
• COBISS.SI-ID: 18344281
• Publication date in RUL: 03.09.2019

REPOVŠ, Dušan and ZAICEV, Mikhail, 2018, ▫$\mathbb{Z}_2$▫-graded codimensions of unital algebras. International journal of algebra and computation [online]. 2018. Vol. 28, no. 3, p. 483–500. [Accessed 11 April 2025]. DOI 10.1142/S0218196718500224. Retrieved from: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=eng&id=109453

Record is a part of a journal

• Title: International journal of algebra and computation
• Shortened title: Int. j. algebra comput.
• Publisher: World Scientific
• ISSN: 0218-1967
• COBISS.SI-ID: 1554709