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Mat. Sb. (N.S.), 1977, Volume 104(146), Number 1(9), Pages 140–150 (Mi msb2940)  

This article is cited in 3 scientific papers (total in 3 papers)

On closed subsets of roots and cohomology of regular subalgebras

F. M. Malyshev


Abstract: This article presents a method of describing the closed subsets of a root system. For example, determining the closed subsets of a root system of type $A_l$ is equivalent to introducing a quasi-ordering on a set of $l+1$ elements. It is shown that the dimensions of the cohomology groups of the corresponding regular subalgebras of $\mathfrak{gl}(l,K)$ in the adjoint representation can be expressed in terms of the Betti numbers of a polyhedron which is constructed by the use of a partial ordering which arises from our quasi-ordering.
Bibliography: 11 titles.

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English version:
Mathematics of the USSR-Sbornik, 1977, 33:1, 125–135

Bibliographic databases:

UDC: 519.48
MSC: Primary 17B20, 18H25; Secondary 06A45, 05C05
Received: 22.11.1976

Citation: F. M. Malyshev, “On closed subsets of roots and cohomology of regular subalgebras”, Mat. Sb. (N.S.), 104(146):1(9) (1977), 140–150; Math. USSR-Sb., 33:1 (1977), 125–135

Citation in format AMSBIB
\Bibitem{Mal77}
\by F.~M.~Malyshev
\paper On closed subsets of roots and cohomology of regular subalgebras
\jour Mat. Sb. (N.S.)
\yr 1977
\vol 104(146)
\issue 1(9)
\pages 140--150
\mathnet{http://mi.mathnet.ru/msb2940}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=472944}
\zmath{https://zbmath.org/?q=an:0365.17006|0397.17006}
\transl
\jour Math. USSR-Sb.
\yr 1977
\vol 33
\issue 1
\pages 125--135
\crossref{https://doi.org/10.1070/SM1977v033n01ABEH002416}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1977GQ33000007}


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  • http://mi.mathnet.ru/eng/msb/v146/i1/p140

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Pommerening K., “Invariant Unipotent Groups”, Math. Z., 176:3 (1981), 359–374  crossref  mathscinet  zmath  isi
    2. N. V. Gravin, D. Yu. Shiryaev, “Abnormal subgroups of classical groups corresponding to closed sets of roots”, J. Math. Sci. (N. Y.), 161:4 (2009), 542–552  mathnet  crossref  zmath  elib
    3. F. M. Malyshev, “Bazisy rekurrentnykh posledovatelnostei”, Chebyshevskii sb., 16:2 (2015), 155–185  mathnet  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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