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 $A$.
Settore MAT/02 - Algebra
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].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/97276
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