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On Trace Bilinear Forms on Lie-Algebras

Published online by Cambridge University Press:  18 May 2009

Hans Zassenhaus
Hans Zassenhaus
Affiliation:
University of Notre Dame, Notre Dame, Indiana, U.S.A.
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To what extent is the structure of a Lie-algebra L over a field F determined by the bilinear form

on L that is derived from a matrix representation

of L with finite degree d(Δ) by forming the trace of the matrix products

Such a bilinear form is a function with two arguments in L, values in F and the properties:

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 4 , Issue 2 , July 1959 , pp. 62 - 72
Copyright
Copyright © Glasgow Mathematical Journal Trust 1959

References

1.Artin, E., Seminar über Lie'sche Ringe, unpublished typewritten notes, Hamburg 1933.Google Scholar
2.Dieudonné, J., On semi-simple Lie-algebras, Proc. Amer. Math. Soc., 4, (1953), 931–932.CrossRefGoogle Scholar
3.Schenkman, E., A theory of subinvariant Lie-algebras, Amer. Journ. of Math., 53, 1951, 453–474.CrossRefGoogle Scholar
4.Zassenhaus, H., Über Lie'sche Ringe mit Primzahlcharakteristik, Abh. Math. Sem. Univ. Hamburg, 13 (1939), 1–100.Google Scholar