Nagoya Mathematical Journal

On homogeneous spaces, holonomy, and non-associative algebras

Arthur A. Sagle

Full-text: Open access

Article information

Source
Nagoya Math. J., Volume 32 (1968), 373-394.

Dates
First available in Project Euclid: 14 June 2005

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1118797390

Mathematical Reviews number (MathSciNet)
MR0231946

Zentralblatt MATH identifier
0159.51503

Subjects
Primary: 22.70

Citation

Sagle, Arthur A. On homogeneous spaces, holonomy, and non-associative algebras. Nagoya Math. J. 32 (1968), 373--394. https://projecteuclid.org/euclid.nmj/1118797390


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References

  • [1] S. Helgason Differential Geometry and Symmetric Spaces, Academic Press, 1962.
  • [2] N.Jacobson Lie Algebras, John Wiley, 1962.
  • [3] N.Jacobson Structure of Rings, American Mathematical Society, 1956.
  • [4] N.Jacobson Completely reducible Lie algebras of linear transformations, Proc. Amer. Math. Soc, Vol. 2 (1951), 105-113.
  • [5] B. Kostant Onholonomy andhomogeneous spaces, Nagoya Math.Jol., Vol. 12(1957), 31-54.
  • [6] O. Loos Thesis, University of Munich,1966.
  • [7] K. Nomizu Recent development in the theory of connections and holonomy groups, Advances in Mathematics, Vol. 1, Academic Press,1961.
  • [8] K. Nomizu Invariant afine connections on homogeneous spaces, Amer. Math.J.,Vol. 76 (1954), 33-65.
  • [9] K. Nomizu Studies on Riemannian homogeneous spaces, Nagoya Math. J., Vol.9 (1955), 43-56.
  • [10] A. Sagle On anti-commutative algebras and homogeneous spaces, to appear J. of Math, andMech.,1967.
  • [1] A. Sagle A note on simple anti-commutative algebras obtained from reductive homo- geneous spaces, toappear in Nagoya Math.J.
  • [12] A. Sagle A note on triple systems and totally geodesic submanifolds in a homogeneous space, to appear in Nagoya Math.J.
  • [13] A. Sagle andD.J.Winter Onhomogeneous spaces andreductive subalgebras of simple Lie algebras, to appear in Trans. Amer. Math. Soc.
  • [14] R.D.Schafer Inner derivations of nonassociative algebras, Bull. Amer. Math. Soc, Vol. 55 (1949), 769-776.
  • [15] J. Wolf Complex homogeneous contact manifolds and quaternionic symmetric spaces, J. of Math, andMech., Vol. 14 (1965), 1033-1042.
  • [16] J. Wolf The geometry and structure of isotropy-irreducible homogeneous spaces, to appear.
  • [17] K. Yamaguti Note onMalcev algebras, KumamotoJ. Sci.,Vol. 5 (1962), 171-184.
  • [18] J. Hano andY. Matsushima Some studies on Kaehlerian homogeneous spaces, Nagoya Math. J.,Vol. 11 (1957), 77-92. University of Minnesota