논문KCI 등재
ENGEL'S AND LIE'S THEOREMS FOR LIE ALGEBRA BUNDLES
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We prove the Engel's structure theorem for a Lie algebra bundle E by proving the existence of a nite dimensional ample Lie subalgebra of Γ(E), the Lie algebra of all sections of E. Further Lie's theorem is proved using the existence of a joint eigenvector in the ample Lie subalgebra of Γ(E) corresponding to a solvable subalgebra bundle X of End(E).
Abstract
We prove the Engel's structure theorem for a Lie algebra bundle E by proving the existence of a nite dimensional ample Lie subalgebra of Γ(E), the Lie algebra of all sections of E. Further Lie's theorem is proved using the existence of a joint eigenvector in the ample Lie subalgebra of Γ(E) corresponding to a solvable subalgebra bundle X of End(E).
참고문헌 (9)
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- H. Gundogan, "Classification and stucture theory of Lie algebras of smooth sections" (2011), Logos Verlag Berlin GmbH
- J. E. Humphreys, "Introduction to Lie algebras and representation theory, volume 9of Graduate Texts in Mathematics" (1978), Springer-Verlag
- B. S. Kiranagi, "Lie algebra bundles", Bull. Sci. Math, 102(1), pp.57~62 (1978)
- B. S. Kiranagi, "Lie algebra bundles and Lie rings", Proc. Nat. Acad. India, 54(A), pp.38~44 (1984)
- R. G. Swan, "Vector bundles and projective modules", Trans. Amer. Math. Soc., 105, pp.264~277 (1962)
관련 논문AI추천
ON THE RADICAL BUNDLE OF A LIE ALGEBRA BUNDLEB.S. Kiranagi, G.PREMA, RANJITHA KUMAR장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2012 · 제15권 제4호ON DERIVATION ALGEBRA BUNDLE OF AN ALGEBRA BUNDLEB. MADHU, B.S. Kiranagi, K. AJAYKUMAR, RANJITHA KUMAR장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2018 · 제21권 제2호Lie algebra bundles and a generalization of Lie group bundlesB.S. Kiranagi, K. AJAYKUMAR장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2019 · 제22권 제4호On pull back Lie algebra bundlesB.S. Kiranagi, RANJITHA KUMAR, R. RAJENDRA장전수학회 · Advanced Studies in Contemporary Mathematics2012 · 제22권 제4호ON MODULE BUNDLES OVER ALGEBRA BUNDLESB. S. KIRANAGI, H. M. PRASAD, R. RAJENDRA장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2021 · 제24권 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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