Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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RADICALS OF A LEFT-SYMMETRIC ALGEBRA ON A NILPOTENT LIE GROUP

  • Chang, Kyeong-Soo (Department of Mathematical Sciences, Seoul National University) ;
  • Kim, Hyuk (Department of Mathematical Sciences, Seoul National University) ;
  • Lee, Hyun-Koo (Department of Mathematical Sciences, Seoul National University)
  • Published : 2004.05.01
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Abstract

The purpose of this paper is to compare the radicals of a left symmetric algebra considered in 〔1〕 when the associated Lie algebra is nilpotent. In this case, we show that all the radicals considered there are equal. We also consider some other radicals and show they are also equal.

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References

  1. Comm. Algebra v.27 no.7 Radicals of a left-symmetric algebra K.S.Chang;H.Kim;H.C.Myung https://doi.org/10.1080/00927879908826619
  2. Mutations of alternative algebras A.Elduque;H.C.Myung
  3. Trans. Amer. Math. Soc. v.295 no.1 Affine manifolds and orbits of algebraic groups W.Goldman;M.Hirsh https://doi.org/10.1090/S0002-9947-1986-0831195-0
  4. Ann. Inst. Fourier(Grenoble) v.29 no.4 Radical d'une algebre symmetrique a gauche J.Helmstetter
  5. J. Differential Geom. v.24 no.3 Complete left-invariant affine structures on nilpotent Lie groups H.Kim
  6. J. Korean math. Soc. v.33 no.4 The geometry of left-symmetric algebra H.Kim
  7. Tensor, N. S. v.36 no.3 On the radical of a left-symmetric algebra A.Mizuhara
  8. Tensor, N. S. v.41 no.1 On the symmetric algebras over a nilpotent complex Lie algebra A.Mizuhara
  9. Tensor, N. S. v.44 no.1 On the radical of a left symmetric algebra Ⅲ A.Mizuhara
  10. Tensor, N. S. v.44 no.2 On left symmetric algebras over a real nilpotent Lie algebra A.Mizuhara
  11. Proc. Amer. Math. Soc. v.47 Translations in certain groups of affine motions J.Scheuneman https://doi.org/10.1090/S0002-9939-1975-0372120-7
  12. Introduction to Lie groups and Lie algebras A.A.Sagle;R.E.Walde
  13. An Introduction to nonassociative algebras Schafer
  14. Math. Ann. v.293 no.3 The structure of complete left-symmetric algebras D.Segal https://doi.org/10.1007/BF01444735

Cited by

  1. Left-symmetric algebras, or pre-Lie algebras in geometry and physics vol.4, pp.3, 2006, https://doi.org/10.2478/s11533-006-0014-9