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 \(dim(V ) \le p^{n^2-1}\).