限制pre-李代数
On Restricted pre-Lie Algebras
研究限制pre-李代数的结构,给出了限制pre-李代数和可限制pre-李代数的定义,得到了限制pre-李代数的p-映射性质和可限制pre-李代数的性质,还讨论了带有半单元的限制pre-李代数及拟环面限制pre-李代数和分解唯一性定理.
The paper studies the structure of restricted pre-Lie algebras. More specifically speaking, we first give the definitions of restricted pre-Lie algebras and restrictable pre-Lie algebras. Second, we obtain some properties of p-mappings and restrictable preLie algebras, and research restricted pre-Lie algebras with semisimple elements. Finally, quasi-toral restricted pre-Lie algebras are discussed and the uniqueness of decomposition for restricted pre-Lie algebras is determined.
可限制pre-李代数 / 半单元 / 环面 {{custom_keyword}} /
restricted pre-Lie algebras / semisimple elements / tori {{custom_keyword}} /
[1] Boyom M. N., The cohomology of Koszul-Vinberg algebras, Pacific J. Math., 2006, 225:119-153.
[2] Chapoton F., Livernet M., Pre-Lie algebras and the rooted trees operad, Int. Math. Res. Not., 2001, 8:395-408.
[3] Chen L. Y., Zhang Y. Z., Meng D. J., On the decomposition of restricted Lie superalgebras (in Chinese), Acta Math. Sci., 2007, 27(A)(4):577-583.
[4] Connes A., Kreimer D., Hopf algebras, renormalization, and noncommutative geometry, Comm. Math. Phys., 1998, 199:203-242.
[5] Dokas I., Pre-Lie algebras in positive characteristic, J. Lie Theory, 2013, 23(4):937-952.
[6] Dokas I., Loday J. L., On restricted Leibniz algebras, Comm. Algebra, 2006, 34:4467-4478.
[7] Farnsteiner R., Note on Frobenius extensions and restricted Lie superalgebras, J. Pure Appl. Algebra, 1996, 108:241-256.
[8] Gerstenhaber M., The cohomology structure of an associative ring, Ann. of Math, 1963, 78:267-288.
[9] Hodge T. L., Lie triple systems, restricted Lie triple systems, and algebraic groups, J. Algebra, 2001, 244:533-580.
[10] Loday J. L., Vallette B., Algebraic Operads, Grundlehren der mathematischen Wissenschaften, 346, SpringerVerlag, Berlin, 2012.
[11] Schedler T., Connes-Kreimer quantizations and PBW theorems for pre-Lie algebras, Soc. Math. France, Paris, 2013, 26:223-251.
[12] Strade H., The classification of the simple modular Lie algebras:Ⅲ, Solution of the classcial case, Ann. Math., 1991, 133:577-604.
[13] Strade H., Farnsteiner R., Modular Lie Algebras and Their Representations, Dekker, New York, 1988.
[14] Zhang C. W., Representations for the restricted Lie color algebras, Algebras Represent. Theory, 2013, 16:445-470.
国家自然科学基金资助项目(11171055,11471090)
/
〈 | 〉 |