Title: How Many Idempotents are Necessary to Generate Matrix Algebras?
Abstract: Considering an upper triangular matrix algebra as a special case of a complete blocked triangular matrix algebra, we show that the ceiling of log n (base 2) is the minimum number of idempotents needed to generate many such algebras, where n denotes the number of 1 x 1 diagonal blocks. We do not know the answer for ("non-complete") blocked triangular matrix algebras. |