Let A be a finite-dimensional algebra over an algebraically closed field with radical square zero, and such that all simple A-modules have dimension at most two. We give a characterization of those A that have finitely many conjugacy classes of left ideals.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm142-1-1, author = {Arkadiusz M\k ecel}, title = {On the finiteness of the semigroup of conjugacy classes of left ideals for algebras with radical square zero}, journal = {Colloquium Mathematicae}, volume = {144}, year = {2016}, pages = {1-49}, zbl = {06497297}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm142-1-1} }
Arkadiusz Męcel. On the finiteness of the semigroup of conjugacy classes of left ideals for algebras with radical square zero. Colloquium Mathematicae, Tome 144 (2016) pp. 1-49. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm142-1-1/