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Zap. Nauchn. Sem. POMI, 2002, Volume 289, Pages 57–62 (Mi znsl1595)  

Variations on a theme of Higman

N. A. Vavilov, V. A. Petrov

Saint-Petersburg State University

Abstract: Let R be an associative ring with 1, $n\ge3$ We show that Higman's computation of the first cohomology group of the special linear group over a field with natural coefficients really shows that $H^1(\operatorname{St}(n,R),R^n)=0$ for $n\ge4$ and explicitly compute this group for $n=3$, when it does not vanish. In [6] the second-named author extended these results to all classical Steinberg groups.

Full text: PDF file (147 kB)

English version:
Journal of Mathematical Sciences (New York), 2004, 124:1, 4708–4710

Bibliographic databases:

UDC: 512.5+512.6+512.7+512.8
Received: 10.06.2002

Citation: N. A. Vavilov, V. A. Petrov, “Variations on a theme of Higman”, Problems in the theory of representations of algebras and groups. Part 9, Zap. Nauchn. Sem. POMI, 289, POMI, St. Petersburg, 2002, 57–62; J. Math. Sci. (N. Y.), 124:1 (2004), 4708–4710

Citation in format AMSBIB
\Bibitem{VavPet02}
\by N.~A.~Vavilov, V.~A.~Petrov
\paper Variations on a theme of Higman
\inbook Problems in the theory of representations of algebras and groups. Part~9
\serial Zap. Nauchn. Sem. POMI
\yr 2002
\vol 289
\pages 57--62
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl1595}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1949733}
\zmath{https://zbmath.org/?q=an:1070.20053}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2004
\vol 124
\issue 1
\pages 4708--4710
\crossref{https://doi.org/10.1023/B:JOTH.0000042306.32825.6a}


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