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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.
After the seminar we will take the speaker to lunch. See the Algebra Seminar web page for information about other seminars in the series. Anthony Henderson anthonyh@maths.usyd.edu.au. |