University of Sydney Algebra Seminar

Donald Barnes (University of Sydney)

Friday 1 April, 12-1pm, Place: Carslaw 375

Faithful completely reducible representation of modular Lie algebras

The Ado-Iwasawa Theorem asserts that a finite-dimensional Lie algebra $L$ over a field $F$ has a finite-dimensional faithful module $V$ . There are several extensions asserting the existence of such a module $V$ with various additional properties. In particular, Jacobson has proved that if the field $F$ has characteristic $p>0$, then there exists a completely reducible such module $V$ . I prove that if $L$ is of dimension $n$ over $F$ of characteristic $p$, then $L$ has a faithful completely reducible module $V$ with $dim(V)\le p^{n^2-1}$.