On cogrowth function of algebras and its logarithmical gap

Translated title of the contribution: On cogrowth function of algebras and its logarithmical gap

Alexei Ya Kanel-Belov, Igor Melnikov, Ivan Mitrofanov

Research output: Contribution to journalArticlepeer-review

Abstract

Let A ≅ k 〉X〈/I be an associative algebra. A finite word over alphabet X is I -reducible if its image in A is a k-linear combination of length-lexicographically lesser words. An obstruction is a subword-minimal I - reducibleword. If the number of obstructions is finite then I has a finite Gröbner basis, and the word problem for the algebra is decidable. A cogrowth function is the number of obstructions of length ≤ n. We show that the cogrowth function of a finitely presented algebra is either bounded or at least logarithmical. We also show that an uniformly recurrent word has at least logarithmical cogrowth.

Translated title of the contributionOn cogrowth function of algebras and its logarithmical gap
Original languageEnglish
Pages (from-to)297-303
Number of pages7
JournalComptes Rendus Mathematique
Volume359
Issue number3
DOIs
StatePublished - 2021

All Science Journal Classification (ASJC) codes

  • General Mathematics

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