nLab Sergei Gelfand

• Mathematics Genealogy page

Selected writings

Introducing what came to be called BGG resolutions of Lie group representations by Verma modules built using regular differential operators:

• Joseph N. Bernstein, Israel M. Gelfand, Sergei I. Gelfand: Differential operators on the base affine space and a study of $\mathfrak{g}$-modules, in: I. M. Gelfand (ed.), Lie groups and their representations, Adam Hilger (1975) 21-64 [pdf, pdf]

On block decomposition of categories of representations:

• Joseph N. Bernstein, Israel M. Gelfand, Sergei I. Gelfand: Category of $\mathfrak{g}$ modules, Funktsionalnyi Analiz i ego Prilozheniya 10 2 (1976) 1-8 [doi:10.1007/BF01077933]

On homological algebra and homotopical algebra (via triangulated categories and including the model structure on dgc-algebras for rational homotopy theory):

• Sergei Gelfand, Yuri Manin, Methods of homological algebra, transl. from the 1988 Russian (Nauka Publ.) original, Springer (1996) xviii+372 pp. 2nd corrected ed. (2002) [doi:10.1007/978-3-662-12492-5]

On quasideterminants:

• Israel M. Gelfand, Sergei Gelfand, Vladimir S. Retakh, Robert Lee Wilson: Quasideterminants, Advances in Mathematics 193 (2005) 56–141 [doi:10.1016/j.aim.2004.03.018]

Related entries

• model structure on dg-algebras

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