Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 1 of 1
Full-Text Articles in Algebra
Writing Representations Over Proper Division Subrings, Stephen P. Glasby
Writing Representations Over Proper Division Subrings, Stephen P. Glasby
All Faculty Scholarship for the College of the Sciences
Let �� be a division ring, and G a finite group of automorphisms of E whose elements are distinct modulo inner automorphisms of ��. Let �� = ��G be the division subring of elements of �� fixed by G. Given a representation p : �� →��d×d of an �� -algebra ��, we give necessary and sufficient conditions for p to be writable over ��. (Here ��d×d denotes the algebra of d×d matrices over ��, and a matrix A writes p over �� if A−1p(��)A ⊆ Fd×d.) We give an algorithm for constructing an …