6533b830fe1ef96bd12970a3
RESEARCH PRODUCT
Varieties with at most cubic growth
S. MishchenkoA. Valentisubject
Algebra and Number TheoryVarietie010102 general mathematicsZero (complex analysis)Field (mathematics)01 natural sciencesCombinatoricsIdentity (mathematics)Settore MAT/02 - Algebra0103 physical sciences010307 mathematical physics0101 mathematicsVariety (universal algebra)Codimension growthMathematicsdescription
Abstract 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 ( y z ) ≡ 0 such that c n ( V ) C n α , with 1 ≤ α 3 , for some constant C. We prove that if 1 ≤ α 2 then c n ( V ) ≤ C 1 n , and if 2 ≤ α 3 , then c n ( V ) ≤ C 2 n 2 , for some constants C 1 , C 2 .
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2019-01-15 |