Group graded algebras and varieties with quadratic codimension growth
Wesley Quaresma Cota

TL;DR
This paper classifies unitary G-graded varieties with quadratic codimension growth, showing they are direct sums of algebras generating minimal G-graded varieties, thus advancing understanding of polynomial identity growth in graded algebras.
Contribution
It provides a classification of G-graded varieties with quadratic codimension growth and describes their structure as direct sums of minimal G-graded varieties.
Findings
Classified varieties generated by unitary algebras with quadratic G-graded codimension growth.
Showed these varieties are direct sums of algebras generating minimal G-graded varieties.
Established that G-graded codimension growth is either polynomial or exponential.
Abstract
Let be an associative algebra graded by a finite group over a field of characteristic zero. One associates to the sequence of -graded codimensions , , which measures the growth of the polynomial identities satisfied by . It is known that this sequence is either polynomially bounded or grows exponentially. In this paper, we study unitary -graded varieties of polynomial codimension growth. In particular, we classify the varieties generated by unitary algebras with quadratic codimension growth and show that these varieties can be described as a direct sums of algebras that generate minimal -graded varieties.
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Taxonomy
TopicsAdvanced Topics in Algebra · Advanced Differential Equations and Dynamical Systems · Commutative Algebra and Its Applications
