6533b86ffe1ef96bd12cdd99
RESEARCH PRODUCT
An uncountable family of almost nilpotent varieties of polynomial growth
A. ValentiS. Mishchenkosubject
Pure mathematicsSecondarySubvarietyUnipotentCentral series01 natural sciencesMathematics::Group TheoryLie algebraFOS: Mathematics0101 mathematicsMathematics::Representation TheoryMathematicsDiscrete mathematicsAlgebra and Number Theory010102 general mathematicsMathematics::Rings and AlgebrasMathematics - Rings and AlgebrasPrimary; Secondary; Algebra and Number Theory010101 applied mathematicsNilpotentSettore MAT/02 - AlgebraRings and Algebras (math.RA)Uncountable setVariety (universal algebra)Nilpotent groupPrimarydescription
A non-nilpotent variety of algebras is almost nilpotent if any proper subvariety is nilpotent. Let the base field be of characteristic zero. It has been shown that for associative or Lie algebras only one such variety exists. Here we present infinite families of such varieties. More precisely we shall prove the existence of 1) a countable family of almost nilpotent varieties of at most linear growth and 2) an uncountable family of almost nilpotent varieties of at most quadratic growth.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2017-01-23 |