Moscow Mathematical Journal
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mosc. Math. J.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Moscow Mathematical Journal, 2019, Volume 19, Number 4, Pages 655–693
DOI: https://doi.org/10.17323/1609-4514-2019-19-4-655-693
(Mi mmj749)
 

This article is cited in 4 scientific papers (total in 4 papers)

On an infinite limit of BGG categories $\mathcal O$

Kevin Coulembiera, Ivan Penkovb

a School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia
b Jacobs University Bremen, 28759 Bremen, Germany
Full-text PDF Citations (4)
References:
Abstract: We study a version of the BGG category $\mathcal{O}$ for Dynkin Borel subalgebras of root-reductive Lie algebras $\mathfrak{g}$, such as $\mathfrak{gl}(\infty)$. We prove results about extension fullness and compute the higher extensions of simple modules by Verma modules. In addition, we show that our category $O$ is Ringel self-dual and initiate the study of Koszul duality. An important tool in obtaining these results is an equivalence we establish between appropriate Serre subquotients of category $O$ for $\mathfrak{g}$ and category $\mathcal{O}$ for finite dimensional reductive subalgebras of $\mathfrak{g}$.
Key words and phrases: BGG Category $\mathcal{O}$, root-reductive Lie algebra, Dynkin Borel subalgebra, Koszul duality, Ringel duality, Verma module, Serre subquotient category, quasi-hereditary algebra.
Funding agency Grant number
Deutsche Forschungsgemeinschaft PE980/7-1
Australian Research Council DE170100623
KC was supported by ARC grant DE170100623. IP was supported in part by DFG grant PE980/7-1.
Bibliographic databases:
Document Type: Article
MSC: 17B65, 16S37, 17B55
Language: English
Citation: Kevin Coulembier, Ivan Penkov, “On an infinite limit of BGG categories $\mathcal O$”, Mosc. Math. J., 19:4 (2019), 655–693
Citation in format AMSBIB
\Bibitem{CouPen19}
\by Kevin~Coulembier, Ivan~Penkov
\paper On an infinite limit of BGG categories $\mathcal O$
\jour Mosc. Math.~J.
\yr 2019
\vol 19
\issue 4
\pages 655--693
\mathnet{http://mi.mathnet.ru/mmj749}
\crossref{https://doi.org/10.17323/1609-4514-2019-19-4-655-693}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000506166200002}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85074729008}
Linking options:
  • https://www.mathnet.ru/eng/mmj749
  • https://www.mathnet.ru/eng/mmj/v19/i4/p655
  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Moscow Mathematical Journal
    Statistics & downloads:
    Abstract page:234
    References:23
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024