Homogeneous Vector Bundles and Koszul Algebras | Zendy

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Homogeneous Vector Bundles and Koszul Algebras

Author(s) -

Hille Lutz

Publication year - 1998

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.19981910109

Subject(s) - mathematics , unipotent , algebraically closed field , quiver , reductive group , algebraic group , vector bundle , pure mathematics , homogeneous , variety (cybernetics) , flag (linear algebra) , abelian group , borel subgroup , algebraic number , abelian variety , group (periodic table) , algebra over a field , combinatorics , group theory , mathematical analysis , statistics , chemistry , organic chemistry

Let G be a reductive algebraic group defined over an algebraically closed field of characteristic zero and let P be a parabolic subgroup of G. We consider the category of homogeneous vector bundles over the flag variety G/P. This category is equivalent to a category of representations of a certain infinite quiver with relations by a generalisation of a result in [BK]. We prove that both categories are Koszul precisely when the unipotent radical P u of P is abelian.

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