References
E. Artin,Geometric Algebra. Interscience Publishers, New York, 1975.
E. Becker, Halbeinfache quadratische Algebren und antikommutative Algebren mit assoziativen Bilinearformen.Abh. Math. Sem. Hamburg36 (1971), 229–256.
———, Über eine Klasse flexibler quadratischer Divisionsalgebren.J. reine angew. Math. 256 (1972), 25–57.
———, Kennzeichnung quasi-alternativer quadratischer Divisionsalgebren.Abh. Math. Sem. Hamburg 38 (1973), 88–105.
W. Benz,Vorlesungen über Geometrie der Algebren. Grundlehren197 Springer- Verlag, Berlin-Heidelberg-New York, 1973.
H. Braun andM. Koecher,Jordan-Algebren. Springer-Verlag, Berlin-New York, 1966.
R. L. H. Griess, The friendly giant.Invent, math.69 (1982), 1–102.
H. Gross,Quadratic Forms in Infinite Dimensional Vector Spaces. Progress in Math.1 Birkhäuser-Verlag, Boston-Basel-Stuttgart, 1979.
T. Grundhöfer, Non-associative division algebras admitting many derivations.Forum Math.2 (1990), 585–601.
K. Harada, On a commutative nonassociative algebra associated with a multiply transitive group.J. Fac. Sci. Univ. Tokyo Sect. IA Math.28 (1981), 843–849.
———, On commutative nonassociative algebras associated with the double transitive permutation groups PSLm(q), m ≽ 3.Comm. Algebra 12 (1984), 2291–2313.
———, On a commutative nonassociative algebra associated with a double transitive group.J. of Algebra 91 (1984), 192–206.
———, Commutative algebras associated with permutative groups.Proceedings of the Rutgers group theory year, 1983–1984 (New Brunswick N.J. 1983-1984), 111–118, Cambridge Univ. Press, Cambridge-New York 1985.
———, Symmetric groups as automorphisms of some commutative algebras.J. of Algebra 94 (1985), 406–410.
I. Kaplansky, Algebras with many derivations; Aspects of Mathematics and it’s Applications, J.A. Barroso ed., 431–438, Elsevier Science Publ. Amsterdam 1986.
H. J. Kowalsky, Topologische Räume. Birkhäuser Verlag, Basel-Stuttgart 1961.
C. Riehm, The equivalence of bilinear forms.J. of Algebra31 (1974), 45–66.
H. Röhrl andS. Walcher, Some classes of algebras and their derivation algebras.Algebras, Groups and Geometries4 (1987), 475–496.
———, Algebras of complexity one.Algebras, Groups and Geometries 5 (1988), 61–107.
R. D. Schafer,An introduction to nonassociative algebras. Academic Press, New York and London 1966.
W. Scharlau,Quadratic forms. Springer-Verlag, Berlin-Heidelberg-New York-Tokyo 1985.
S. D. Smith, Nonassociative commutative algebras for triple covers of 3-transposition groups.Michigan Math. J.24 (1977), 273–287.
H. Suzuki, Commutative algebras associated with a double transitive group.Osaka J. Math.23 (1986), 541–561.
A. Voigt andJ. Wloka,Hilberträume und elliptische Differentialoperatoren. BI, Mannheim-Wien-Zürich 1975.
G. E. Wall, On the conjugacy classes in the unitary, symplectic and orthogonal groups.J. Austral. Math. Soc.3 (1963), 1–62.
S. Warner,Topological fields. North-Holland Math. Studies 157, North-Holland, Amsterdam-New York-Oxford-Tokyo 1989.
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1991Mathematics Subject Classification. 17A60; 51F25; 17C99; 17B99; 17A30; 17A45. The first author was supported by NSERC.
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Brungs, H.H., Strambach, K. Algebras and orthogonal groups I. Abh.Math.Semin.Univ.Hambg. 66, 11–54 (1996). https://doi.org/10.1007/BF02940793
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DOI: https://doi.org/10.1007/BF02940793