FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2024935720> ?p ?o ?g. }

• W2024935720 endingPage "335" @default.
• W2024935720 startingPage "335" @default.
• W2024935720 abstract "Let g be a finite dimensional, complex, semisimple Lie algebra and let V be a finite dimensional, irreducible g-module. By computing a certain Lie algebra cohomology we show that the generalized versions of the weak and the strong Bemstein-Gelfand-Gelfand resolutions of V obtained by H. Garland and J. Lepowsky are identical. Let G be a real, connected, semisimple Lie group with finite center. As an application of the equivalence of the generalized Bernstein-Gelfand-Gelfand resolutions we obtain a complex in terms of the degenerate principal series of G, which has the same cohomology as the de Rham complex. Introduction. Let g be a finite dimensional, complex, semisimple Lie algebra and let V be a finite dimensional, irreducible g-module. In [2, Theorem 9.9], I. N. Bernstein, I. M. Gelfand and S. I. Gelfand constructed a resolution of V by certain a-modules with Verma composition series. In the same paper another resolution of V is constructed which resolves V by direct sums of Verma modules, improving Theorem 9.9. (Cf. [2, Theorem 10.1'].) In their work, Bernstein, Gelfand and Gelfand study systematically a certain category of g-modules known as the category 0. Both the weak and the strong resolutions were generalized by H. Garland and J. Lepowsky in the papers [9] and [14] where generalized Verma modules play the same role as Verma modules in [2]. We will refer to these resolutions as the generalized weak BGG resolution and the generalized strong BGG resolution. In this paper we prove that the two generalized BGG resolutions are identical. Our main theorem, Theorem 9.3 shows that each g-module in the generalized weak BGG resolution splits into a direct sum of generalized Verma modules. Consequently each such g-module is isomorphic to the g-module at the corresponding level in the generalized strong BGG resolution. One of our methods consists in studying a certain category of a-modules and later using such category as a framework in order to obtain a key lemma, Lemma 9.1. We would like to point out that, in the light of Yoneda's interpretation of cohomology, Lemma 9.1 implies vanishing theorems on Lie algebra cohomology. (See the remark following the proof of Lemma 9.1.) Received by the editors November 21, 1978 and, in revised form, May 21, 1979. 1980 Mathematics Subject Classification. Primary 22E47, 17B 10, 17B35, 22E46. ? 1980 American Mathematical Society 0002-9947/80/0000-0551 /$09.00" @default.
• W2024935720 created "2016-06-24" @default.
• W2024935720 creator A5061726692 @default.
• W2024935720 date "1980-02-01" @default.
• W2024935720 modified "2023-09-25" @default.
• W2024935720 title "Splitting criteria for $mathfrak{g}$-modules induced from a parabolic and the Berňste{ui}n-Gel’fand-Gel’fand resolution of a finite-dimensional, irreducible $mathfrak{g}$-module" @default.
• W2024935720 cites W1513971458 @default.
• W2024935720 cites W1528521152 @default.
• W2024935720 cites W1565930783 @default.
• W2024935720 cites W1607402086 @default.
• W2024935720 cites W2039660064 @default.
• W2024935720 cites W2051458282 @default.
• W2024935720 cites W2065402438 @default.
• W2024935720 cites W2081687319 @default.
• W2024935720 cites W2084311720 @default.
• W2024935720 cites W2087961595 @default.
• W2024935720 cites W2088040177 @default.
• W2024935720 cites W2092272609 @default.
• W2024935720 cites W2335683436 @default.
• W2024935720 cites W2602557022 @default.
• W2024935720 cites W3043060850 @default.
• W2024935720 cites W3143309016 @default.
• W2024935720 doi "https://doi.org/10.1090/s0002-9947-1980-0586721-0" @default.
• W2024935720 hasPublicationYear "1980" @default.
• W2024935720 type Work @default.
• W2024935720 sameAs 2024935720 @default.
• W2024935720 citedByCount "86" @default.
• W2024935720 countsByYear W20249357202012 @default.
• W2024935720 countsByYear W20249357202013 @default.
• W2024935720 countsByYear W20249357202014 @default.
• W2024935720 countsByYear W20249357202015 @default.
• W2024935720 countsByYear W20249357202016 @default.
• W2024935720 countsByYear W20249357202017 @default.
• W2024935720 countsByYear W20249357202018 @default.
• W2024935720 countsByYear W20249357202020 @default.
• W2024935720 countsByYear W20249357202021 @default.
• W2024935720 crossrefType "journal-article" @default.
• W2024935720 hasAuthorship W2024935720A5061726692 @default.
• W2024935720 hasBestOaLocation W20249357201 @default.
• W2024935720 hasConcept C136119220 @default.
• W2024935720 hasConcept C138268822 @default.
• W2024935720 hasConcept C154945302 @default.
• W2024935720 hasConcept C189612460 @default.
• W2024935720 hasConcept C202444582 @default.
• W2024935720 hasConcept C2778052762 @default.
• W2024935720 hasConcept C33923547 @default.
• W2024935720 hasConcept C41008148 @default.
• W2024935720 hasConcept C51568863 @default.
• W2024935720 hasConcept C5475112 @default.
• W2024935720 hasConcept C78606066 @default.
• W2024935720 hasConcept C81999800 @default.
• W2024935720 hasConceptScore W2024935720C136119220 @default.
• W2024935720 hasConceptScore W2024935720C138268822 @default.
• W2024935720 hasConceptScore W2024935720C154945302 @default.
• W2024935720 hasConceptScore W2024935720C189612460 @default.
• W2024935720 hasConceptScore W2024935720C202444582 @default.
• W2024935720 hasConceptScore W2024935720C2778052762 @default.
• W2024935720 hasConceptScore W2024935720C33923547 @default.
• W2024935720 hasConceptScore W2024935720C41008148 @default.
• W2024935720 hasConceptScore W2024935720C51568863 @default.
• W2024935720 hasConceptScore W2024935720C5475112 @default.
• W2024935720 hasConceptScore W2024935720C78606066 @default.
• W2024935720 hasConceptScore W2024935720C81999800 @default.
• W2024935720 hasIssue "2" @default.
• W2024935720 hasLocation W20249357201 @default.
• W2024935720 hasOpenAccess W2024935720 @default.
• W2024935720 hasPrimaryLocation W20249357201 @default.
• W2024935720 hasRelatedWork W1519011338 @default.
• W2024935720 hasRelatedWork W1548459773 @default.
• W2024935720 hasRelatedWork W1656036914 @default.
• W2024935720 hasRelatedWork W1674711990 @default.
• W2024935720 hasRelatedWork W169573128 @default.
• W2024935720 hasRelatedWork W1699138565 @default.
• W2024935720 hasRelatedWork W1986067975 @default.
• W2024935720 hasRelatedWork W1989372642 @default.
• W2024935720 hasRelatedWork W1995825433 @default.
• W2024935720 hasRelatedWork W2021213480 @default.
• W2024935720 hasRelatedWork W2042047056 @default.
• W2024935720 hasRelatedWork W2073215282 @default.
• W2024935720 hasRelatedWork W2084061070 @default.
• W2024935720 hasRelatedWork W2088040177 @default.
• W2024935720 hasRelatedWork W2120238531 @default.
• W2024935720 hasRelatedWork W2146927814 @default.
• W2024935720 hasRelatedWork W2153867292 @default.
• W2024935720 hasRelatedWork W2162637896 @default.
• W2024935720 hasRelatedWork W2577114388 @default.
• W2024935720 hasRelatedWork W606654790 @default.
• W2024935720 hasVolume "262" @default.
• W2024935720 isParatext "false" @default.
• W2024935720 isRetracted "false" @default.
• W2024935720 magId "2024935720" @default.
• W2024935720 workType "article" @default.