6533b851fe1ef96bd12a9833

RESEARCH PRODUCT

Graded polynomial identities and exponential growth

Eli AljadeffDaniela La MattinaAntonino Giambruno

subject

Pure mathematicsPolynomialMathematics::Commutative AlgebraApplied MathematicsGeneral MathematicsMathematics::Rings and AlgebrasMathematics - Rings and AlgebrasSettore MAT/02 - Algebra16R10 16W50 16P90Exponential growthRings and Algebras (math.RA)FOS: Mathematicsgraded algebra polynomial identity growth codimensionsMathematics

description

Let $A$ be a finite dimensional algebra over a field of characteristic zero graded by a finite abelian group $G$. Here we study a growth function related to the graded polynomial identities satisfied by $A$ by computing the exponential rate of growth of the sequence of graded codimensions of $A$. We prove that the $G$-exponent of $A$ exists and is an integer related in an explicit way to the dimension of a suitable semisimple subalgebra of $A$.

yearjournalcountryeditionlanguage
2009-03-10
10.1515/crelle.2011.004http://hdl.handle.net/10447/97276