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Cayley Groups
Algebra & Discrete Mathematics| Speaker: | Nicole Lemire, University of Western Ontario |
| Location: | 693 Kerr |
| Start time: | Fri, Oct 29 2004, 12:10PM |
Description
An algebraic group G is called Cayley if there exists
a birational isomorphism
between G and its Lie algebra g which is equivariant
with respect to the conjugation action of G on itself and the
adjoint action of G on g.
Cayley was the first to construct such a birational equivalence for
SO_n. Luna asked whether
or not maps with these properties can be constructed for other
algebraic groups. We prove that
the answer to Luna's question is usually ''no'' with a few exceptions.
In particular, a Cayley map for the group SL_n exists if and only if
n \le 3. The negative results are proved by methods of integral
representation theory.