## University of Sydney Algebra Seminar

# Donald Barnes (University of Sydney)

## Friday 26th April, 12:05-12:55pm, Carslaw 373

### Character clusters for Lie algebra modules over a field of non-zero characteristic

For a Lie algebra \(L\) over an algebraically closed field of non-zero characteristic, every finite-dimensional \(L\)-module can be decomposed into a direct sum of submodules such that all composition factors of a summand have the same character. Using the concept of a character cluster, I generalise this to fields which are not algebraically closed. I also use clusters to generalise the construction of induced modules.