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Algebras with finitely many conjugacy classes of left ideals versus algebras of finite representation type

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Let A be a finite dimensional algebra over an algebraically closed field with the radical nilpotent of index 2. It is shown that A has finitely many conjugacy classes of… Click to show full abstract

Let A be a finite dimensional algebra over an algebraically closed field with the radical nilpotent of index 2. It is shown that A has finitely many conjugacy classes of left ideals if and only if A is of finite representation type provided that all simple A-modules have dimension at least 6.

Keywords: finite representation; finitely many; many conjugacy; classes left; left ideals; conjugacy classes

Journal Title: Journal of Pure and Applied Algebra
Year Published: 2019

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