Stephen Glasby (Central Washington University)

Friday 17th August, 12.05-12.55pm, Carslaw 373

Writing projective representations over subfields

Let F be a subfield of a field E, and let A be an F-subalgebra of the full matrix algebra, M(d,E), of d×d matrices over E. When is A conjugate to a subalgebra of M(d,F) modulo scalar matrices in E? If so, how does one find a conjugating matrix? These question arise naturally, and commonly, when computing with matrix groups and algebras. Two different solutions will be presented: one related to a noncommutative version of Hilbert's Satz 90, and one related to the MeatAxe algorithm. The talk will be elementary, and will include simple examples.