The classification of blocks in BGG category
K Coulembier - Mathematische Zeitschrift, 2020 - Springer
Mathematische Zeitschrift, 2020•Springer
We classify all equivalences between the indecomposable abelian categories which appear
as blocks in BGG category OO for reductive Lie algebras. Our classification implies that a
block in category OO only depends on the Bruhat order of the relevant parabolic quotient of
the Weyl group. As part of the proof, we observe that any finite dimensional algebra with
simple preserving duality admits at most one quasi-hereditary structure.
as blocks in BGG category OO for reductive Lie algebras. Our classification implies that a
block in category OO only depends on the Bruhat order of the relevant parabolic quotient of
the Weyl group. As part of the proof, we observe that any finite dimensional algebra with
simple preserving duality admits at most one quasi-hereditary structure.
Abstract
We classify all equivalences between the indecomposable abelian categories which appear as blocks in BGG category for reductive Lie algebras. Our classification implies that a block in category only depends on the Bruhat order of the relevant parabolic quotient of the Weyl group. As part of the proof, we observe that any finite dimensional algebra with simple preserving duality admits at most one quasi-hereditary structure.
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