Abstract:
Integral invariant lattices associated with the standard orthogonal decomposition of a Lie algebra of type Apm−1Apm−1 are described up to similarity. Duality in the class of invariant lattices is studied. Even unimodular root-free lattices of dimension p2m−1p2m−1 are distinguished.
\Bibitem{Abd93}
\by K.~S.~Abdukhalikov
\paper Integral invariant lattices in Lie algebras of type $A_{p^m-1}$
\jour Russian Acad. Sci. Sb. Math.
\yr 1994
\vol 78
\issue 2
\pages 447--478
\mathnet{http://mi.mathnet.ru/eng/sm980}
\crossref{https://doi.org/10.1070/SM1994v078n02ABEH003480}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1225979}
\zmath{https://zbmath.org/?q=an:0819.17008}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1994PD76700012}
Linking options:
https://www.mathnet.ru/eng/sm980
https://doi.org/10.1070/SM1994v078n02ABEH003480
https://www.mathnet.ru/eng/sm/v184/i4/p61
This publication is cited in the following 4 articles:
K. Abdukhalikov, “The Permutation Modules for Finite (Affine) General Linear Groups”, Journal of Mathematical Sciences (New York), 131:5 (2005), 5867
K. S. Abdukhalikov, “Automorphism groups of invariant lattices in the Steinberg module of groups of Lie type of odd characteristic”, Sb. Math., 189:9 (1998), 1273–1294
K. S. Abdukhalikov, “Modular permutation representations of $\operatorname {PSL}(n,p)$”, Sb. Math., 188:8 (1997), 1107–1117
K. S. Abdukhalikov, “Integral lattices associated with a finite affine group”, Russian Acad. Sci. Sb. Math., 83:2 (1995), 431–443
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