Growth curves for algebras
This paper studies matrix representations of algebras (over a field) using countably-infinite matrices which are both row and column finite, and in which the bandwidth growth is controlled. The ideas lead naturally to a concept of "growth of an algebra", somewhat analogous to the growth associated with GK-dimension. They also lead in a similar way to a dimension function on general algebras, which we term bandwidth dimension. For each real number r ∈ [0,1], we construct an algebra having bandwidth dimension precisely r. Since the free algebra turns out to have bandwidth dimension 0, our new dimension promises to distinguish among algebras of infinite GK-dimension.
SubjectsField of Research::01 - Mathematical Sciences::0101 - Pure Mathematics
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