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Radicals of a left-symmetric algebra on a nilpotent Lie group

김혁|이현구|장경수
대한수학회 (The Korean Mathematical Society)|2004.05|대한수학회보 (Bulletin of the KMS)|제41권 제2호|pp. 359-369

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참고문헌

주제분류수학

초록

Abstract

The purpose of this paper is to compare the radicals ofa left symmetric algebra considered in [1] when the associated Liealgebra is nilpotent. In this case, we show that all the radicalsconsidered there are equal. We also consider some other radicalsand show they are also equal.

참고문헌 (12)

  1. "H. C. Myung \paper Radicals of a left-symmetric algebra \jour Comm. Algebra \vol 27 \issue 7 \yr 1999 \pages 3161--3175"
  2. "M. Hirsh \paper Affine manifolds and orbits of algebraic groups \jour Trans. Amer. Math. Soc. \vol 295 \issue 1 \yr 1986 \pages 175--198"
  3. "Kim \paper Complete left-invariant affinestructures on nilpotent Lie groups \jour J. Differential Geom. \vol 24 \issue 3 \yr 1986 \pages 373--394"
  4. "The geometry of left-symmetric algebra", 33, pp.1047~1067
  5. "Mizuhara \paper On the radical of aleft-symmetric algebra \jour Tensor"
  6. "On left symmetric algebras over anilpotent complex Lie algebra \jour Tensor"
  7. "Mizuhara \paper On the radical of a leftsymmetric algebra III \jour Tensor"
  8. "On left symmetric algebras over a realnilpotent Lie algebra \jour Tensor"
  9. "Scheuneman \paper Translations in certaingroups of affine motions \jour Proc. Amer. Math. Soc. \vol 47 \yr 1975 \pages 223--228"
  10. "R. E. Walde \book Introduction to Lie groups and Lie algebras \publ Academic Press \publaddr \vol \yr 1973 \pages"
  11. "Schafer \book An Introduction to Nonassociative algebras \publ Academic Press \publaddr New York \vol \yr 1966 \pages"
  12. "Segal \paper The structure of completeleft-symmetric algebras \jour Math. Ann \vol 293 \issue 3 \yr 1992 \pages 569--578"

관련 논문AI추천

On the nilpotency of certain subalgebras of Kac-Moody algebras of type A_N^{(r)}Seungkeun Min, Yeonok Kim대한수학회 · 대한수학회논문집2003 · 제18권 제3호Some results on non-associative algebras왕문옥, 이광석, 황진구대한수학회 · 대한수학회보2007 · 제44권 제1호ON THE RADICAL BUNDLE OF A LIE ALGEBRA BUNDLEB.S. Kiranagi, G.PREMA, RANJITHA KUMAR장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2012 · 제15권 제4호THE CLASSIFICATION OF ω-LEFT-SYMMETRIC ALGEBRAS IN LOW DIMENSIONSYang Wu, Zhiqi Chen대한수학회 · 대한수학회보2023 · 제60권 제3호On the structure of factor Lie algebrasFarhad Panbehkar, Hesam Safa, Homayoon Arabyani대한수학회 · 대한수학회보2017 · 제54권 제2호Classification of solvable lie algebras whose non-trivial coadjoint orbits of simply connected lie groups are all of codimension 2Hieu Van Ha, Hoa Duong Quang, Tu Thi Cam Nguyen, Vu Anh Le대한수학회 · 대한수학회지2023 · 제60권 제4호

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