The Representation Dimension of a Class of Tame Algebras
Ibrahim Assem, Fl\'avio U. Coelho (IME), Sonia Trepode
TL;DR
This paper proves that strongly simply connected algebras of polynomial growth have a representation dimension at most three, indicating a bound on their complexity.
Contribution
It establishes that such algebras are torsionless-finite and provides a bound on their representation dimension, advancing understanding of their structure.
Findings
A is torsionless-finite
Representation dimension of A is at most three
Results apply to strongly simply connected algebras of polynomial growth
Abstract
We prove that, if A is a strongly simply connected algebra of polynomial growth, then A is torsionless-finite. In particular, its representation dimension is at most three.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Advanced Operator Algebra Research