The Strong Bernstein-Gelfand-Gelfand Resolution for Generalized Kac-Moody Algebras, I — The Existence of the Resolution | Zendy

Satoshi Naito | Zendy

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The Strong Bernstein-Gelfand-Gelfand Resolution for Generalized Kac-Moody Algebras, I — The Existence of the Resolution

Author(s) -

Satoshi Naito

Publication year - 1993

Publication title -

publications of the research institute for mathematical sciences

Language(s) - English

Resource type - Journals

eISSN - 1663-4926

pISSN - 0034-5318

DOI - 10.2977/prims/1195166746

Subject(s) - mathematics , resolution (logic) , pure mathematics , class (philosophy) , lie algebra , cartan matrix , matrix (chemical analysis) , set (abstract data type) , square (algebra) , algebra over a field , series (stratigraphy) , lie conformal algebra , non associative algebra , geometry , artificial intelligence , computer science , paleontology , materials science , composite material , biology , programming language

The purpose of this series of works is to show the existence of the strong Bernstein-Gelfand-Gelfand resolution (cf. [1]) of the irreducible highest weight module L(A) with dominant integral highest weight A over a symmetrizable generalized Kac-Moody algebra ( = GKM algebra). Here, GKM algebras are a class of contragredient Lie algebras Q(A) over C (see [4], [8], or [7, Chapter 1]) associated to a real square matrix A = (aij)ijel indexed by a finite set / which satisfies the conditions:

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