A generalization of the Kantor-Koecher-Titsconstruction 1

@article{Palmkvist2008AGO,
  title={A generalization of the Kantor-Koecher-Titsconstruction 1},
  author={Jakob Palmkvist},
  journal={Journal of Generalized Lie Theory and Applications},
  year={2008},
  volume={2},
  pages={226-230}
}
  • Jakob Palmkvist
  • Published 17 August 2013
  • Mathematics
  • Journal of Generalized Lie Theory and Applications
The Kantor-Koecher-Tits construction associates a Lie algebra to any Jordan algebra. We generalize this construction to include also extensions of the associated Lie algebra. In particular, the conformal realization of so(p + 1, q + 1) generalizes to so(p + n, q + n), for arbitrary n, with a linearly realized subalgebra so(p, q). We also show that the construction applied to 3 × 3 matrices over the division algebras R, C, H, O gives rise to the exceptional Lie algebras f4, e6, e7, e8, as well… 

Octonions, Exceptional Jordan Algebra and The Role of The Group $$F_4$$F4 in Particle Physics

Normed division rings are reviewed in the more general framework of composition algebras that include the split (indefinite metric) case. The Jordan–von Neumann–Wigner classification of finite

References

SHOWING 1-10 OF 10 REFERENCES

Imbedding of Jordan Algebras Into Lie Algebras. II

On Compact Generalized Jordan Triple Systems of the Second Kind

$(uv(xyz))=((uvx)yz)-(x(vuy)z)+(xy(uvz))$ is valid for $u,$ $v,$ $x,$ $y,$ $z\in U$. If, in addition, the relation $(xyz)=(zyx)$ holds for $x,$ $y,$ $z\in U$, then $B$ is said to be a Jordan triple

Une Classe D'Algebres De Lie En Relation Avec Les Algebres De Jordan

Division algebras, (pseudo)orthogonal groups and spinors

The groups SO( nu -1), SO( nu ), SO( nu +1), SO( nu +1, 1) and SO( nu +2, 2) ( nu =1, 2, 4, 8) and their spin representations are described in terms of the division algebras R, C, H and O.

A realization of the Lie Algebra associated to a Kantor triple system

We present a nonlinear realization of the 5-graded Lie algebra associated to a Kantor triple system. Any simple Lie algebra can be realized in this way, starting from an arbitrary 5-grading. In

Conformal and Quasiconformal Realizations¶of Exceptional Lie Groups

Abstract: We present a nonlinear realization of E8(8) on a space of 57 dimensions, which is quasiconformal in the sense that it leaves invariant a suitably defined “light cone” in ℝ57. This

Generalized conformal realizations of Kac–Moody algebras

We present a construction which associates an infinite sequence of Kac–Moody algebras, labeled by a positive integer n, to one single Jordan algebra. For n=1, this reduces to the well known

Imbedding of Jordan algebras into Lie algebras I. Amer

  • J. Math
  • 1967

Some generalizations of Jordan algebras

  • Trudy Sem. Vektor. Tenzor. Anal
  • 1972

Classification of irreducible transitively differential groups

  • Soviet Math. Dokl
  • 1964