Varieties with at most cubic growth

Angela Valenti, Sergey Mishchenko

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


Let V be a variety of non necessarily associative algebras over a field of characteristic zero. The growth of V is determined by the asymptotic behavior of the sequence of codimensions c(n) (V),n = 1,2,..., and here we study varieties of polynomial growth. We classify all possible growth of varieties V of algebras satisfying the identity x(yz) equivalent to 0 such that c(n) (V) < C-n(alpha) with 1 <= alpha < 3, for some constant C. We prove that if 1 <= alpha < 2 then c(n) (V) <= C-1n, and if 2 <= alpha < 3, then c(n)(V) <= C(2)n(2), for some constants C-1, C-2.
Original languageEnglish
Pages (from-to)321-342
Number of pages22
JournalJournal of Algebra
Publication statusPublished - 2019

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory


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