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For a Lie algebra L over an algebraically closed field of non-zerocharacteristic, every finite-dimensional L-module can be decomposed into adirect sum of submodules such that all composition factors of a summand havethe same character. Using the concept of a character cluster, this result isgeneralised to fields which are not algebraically closed. Clusters are used togeneralise the construction of induced modules.

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