Graded polynomial identities and exponential growth
By E. Aljadeff, Antonio Giambruno, D. La Mattina. 2009
75 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/fa038a412066ecdc630dc5b992395658ccae9cc4
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Algebra and Number Theory
In Computational Theory and Mathematics
In Geometry and Topology
Citations in the corpus
- Amitsur's conjecture for associative algebras with a generalized Hopf action (2012, background): “e holds for graded codimensions, G- and H-codimensions. The analog of Amitsur’s conjecture for codimensions of graded identities was proved in 2010–2011 by E. Aljadeff, A. Giambruno, and D. La Mattina [1, 2, 13] for all associative PI-algebras graded by a finite group. As a consequence, they proved th”
- Multialternating graded polynomials and growth of polynomial identities (2012, background): “Id G(A). It was known that the sequence cG n (A), n = 1,2,..., is exponentially bounded ([10]), but only recently its exponential rate of growth was captured in case G is an abelian group. In fact in [1] for finitely generated algebras and in [9] in general, it was shown that if A is any G-graded PI-”