6533b7d6fe1ef96bd1265b16
RESEARCH PRODUCT
Group graded algebras and almost polynomial growth
A. Valentisubject
Algebra and Number TheoryGraded algebra Polynomial identity Growth CodimensionsMathematics::Commutative AlgebraSubalgebraUniversal enveloping algebraGrowthPolynomial identityGraded algebraCodimensionsGraded Lie algebraFiltered algebraCombinatoricsSettore MAT/02 - AlgebraDifferential graded algebraDivision algebraAlgebra representationCellular algebraMathematicsdescription
Let F be a field of characteristic 0, G a finite abelian group and A a G-graded algebra. We prove that A generates a variety of G-graded algebras of almost polynomial growth if and only if A has the same graded identities as one of the following algebras: (1) FCp, the group algebra of a cyclic group of order p, where p is a prime number and p||G|; (2) UT2G(F), the algebra of 2×2 upper triangular matrices over F endowed with an elementary G-grading; (3) E, the infinite dimensional Grassmann algebra with trivial G-grading; (4) in case 2||G|, EZ2, the Grassmann algebra with canonical Z2-grading.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2011-05-01 |