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BIRS Workshop Lecture Videos

Subalgebras generated by idempotents (joint work with Yoav Segev) Rowen, Louis


In 1981, Laffey described subalgebras of associative algebras generated by two idempotents, and showed that central simple algebras (other than division algebras) can be generated by three idempotents. We describe his structure more precisely, as a direct product of Azumaya algebras and a PI-algebra satisfying the identity $(xy - yx)^n,$ and, following an idea of Shestakov, show that Jordan subalgebras of a finite dimensional algebra generated by $n$ completely primitive idempotents algebraic are of dimension $\le 2^n -1.$

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