Seminar series
Date
Thu, 05 Nov 2009
Time
14:30 -
15:30
Location
L3
Speaker
Erik Darpo
Organisation
Oxford/Uppsala
The transformation algebra of an algebra A is the subalgebra of the
algebra of linear endomorphisms of A generated by all left and right
multiplications with elements in A. It was introduced by Albert as a part
of an effort to create a unified structure theory for non-associative
algebras.
One problem with the transformation algebra is that it is a very crude
invariant for general algebras. In the talk, I shall suggest a way to
compensate for this and show that by adding certain information, the
transformation algebra can be used to give a complete picture of the
category of unital division algebras of fixed (finite) dimension over a
field.