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 $A$.
Aljadeff, E., Giambruno, A., La Mattina, D. (2011). Graded polynomial identities and exponential growth. JOURNAL FÜR DIE REINE UND ANGEWANDTE MATHEMATIK, 650, 83-100 [10.1515/CRELLE.2011.004].
Graded polynomial identities and exponential growth
GIAMBRUNO, Antonino;LA MATTINA, Daniela
2011-01-01
Abstract
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 $A$.
| File | Dimensione | Formato | |
|---|---|---|---|
|
Aljadeff,Giambruno,LaMattina-2011-CRELLE.pdf
Solo gestori archvio
Dimensione
175.58 kB
Formato
Adobe PDF
|
175.58 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
