Displaying similar documents to “Composition-diamond lemma for modules”

On representations of restricted Lie superalgebras

Yu-Feng Yao (2014)

Czechoslovak Mathematical Journal

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Simple modules for restricted Lie superalgebras are studied. The indecomposability of baby Kac modules and baby Verma modules is proved in some situation. In particular, for the classical Lie superalgebra of type A ( n | 0 ) , the baby Verma modules Z χ ( λ ) are proved to be simple for any regular nilpotent p -character χ and typical weight λ . Moreover, we obtain the dimension formulas for projective covers of simple modules with p -characters of standard Levi form.

Classification of irreducible weight modules

Olivier Mathieu (2000)

Annales de l'institut Fourier

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Let 𝔤 be a reductive Lie algebra and let 𝔥 be a Cartan subalgebra. A 𝔤 -module M is called a if and only if M = ⊕ λ M λ , where each weight space M λ is finite dimensional. The main result of the paper is the classification of all simple weight 𝔤 -modules. Further, we show that their characters can be deduced from characters of simple modules in category 𝒪 .