The transformation algebra of a division algebra
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Thu, 05/11/2009 14:30 |
Erik Darpo (Oxford/Uppsala) |
Representation Theory Seminar  |
L3 |
| 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. | |||