Pseudocompact algebras and highest weight categories

Details Pseudocompact algebras and highest weight categories Pseudocompact algebras and highest weight categories

2011-04-18

arxiv.org/abs/1104.3373v1

Mathematics

Rings and Algebras

43 pages

Scientific paper

We develop a new approach to highest weight categories $\cal{C}$ with good (and cogood) posets of weights via pseudocompact algebras by introducing ascending (and descending) quasi-hereditary pseudocompact algebras. For $\cal{C}$ admitting a Chevalley duality, we define and investigate tilting modules and Ringel duals of the corresponding pseudocompact algebras. Finally, we illustrate all these concepts on an explicit example of the general linear supergroup $GL(1|1)$.

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