李Rinehart代数的子代数若干性质
Some Properties of Subalgebras of Lie-Rinehart Algebras
本文主要把李代数的c-可补、E-代数的性质以及Frattini理论推广到更为广泛的李Rinehart代数,得到它们的若干性质,给出了可解李Rinehart代数的一个必要条件.同时,分别获得判断c-可补李Rinehart代数和E-李Rinehart代数的一个充分必要条件.
We develop c-supplemented subalgebras, E-algebras and Frattini theory of Lie algebras for Lie-Rinehart algebras, obtain its some important properties and give a necessary conditions for solvable Lie-Rinehart algebras. Moreover, we obtain a necessary and sufficient conditions for E-Lie-Rinehart algebras and c-supplemented Lie-Rinehart algebras, respectively.
李Rinehart代数 / c-可补李Rinehart代数 / E-李Rinehart代数 / Frattini子代数 {{custom_keyword}} /
Lie-Rinehart algebras / c-supplemented Lie-Rinehart algebras / E-Lie-Rinehart algebras / Frattini subalgebras {{custom_keyword}} /
[1] Casas J., Ladra M., Pirashvili T., Crossed modules for Lie-Rinehart algebras, J. Algebra, 2004, 274:192-201.
[2] Casas J., Obstructions to Lie-Rinehart Algebra Extensions, Algebra Colloq., 201118:83-104.
[3] Chen Z., Liu Z., Zhong D., Lie-Rinehart bialgebras for crossed products, J. Pure Appl. Algebra, 2011, 215:1270-1283.
[4] Dokas I., Cohomology of restricted Lie-Rinehart algebras and the Brauer group, Adv. Math., 2012, 231:2573-2592.
[5] Helge M., Chern classes and Lie-Rinehart algebras, Indag. Math., 2007, 18:589-599.
[6] Herz J., Pseudo-algèbras de Lie, C. R. Acad. Sci. Paris, 1953, 236:1935-1937.
[7] Huebschmann J., Extensions of Lie-Rinehart Algebras and the Chern-Weil Construction, Contemp. Amer. Math. Soc., 1999, 227:145-176.
[8] Huebschmann J., Poisson cohomology and quantization, J. Reine Angew. Math., 1990, 408:57-113.
[9] Sun B., Chen L., Restricted and quasi-toral restricted Lie-Rinehart algebras, Open Math., 2015:518-527.
[10] Song H., Zhou J., Chen L., C-supplemented subalgebras of Lie supertriple systems and E-Lie supertriple systemsc, Journal of Jilin University (Science Edition), 2012, 50(4):681-685.
[11] Tomasz M., A Pairing Between Super Lie-Rinehart and Periodic Cyclic Homology, Commun. Math. Phys., 2006, 263(3):737-747.
[12] Wu X., Chen L., The Frattini subsystem of a Lie supertriple system, J. Math. Res. Exposition, 2010, 30(3):399-406.
[13] Wu X., Chen L., C-supplemented subalgebras of a Lie superalgebra, Adv. Math. China, 2011, 40(4):407-412.
[14] Wu X., Zhao X., Zhou L., et al., Some properties of solvable δ-Lie supertriple system, Journal of Jilin University (Science Edition), 2016, 54(6):1205-1209.
国家自然科学基金资助项目(11771069);吉林省自然科学基金资助项目(20170101048JC)及吉林省教育厅项目(JJKH20180005K)
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