具有平凡中心的限制李Rinehart代数的分解
|
摘要
证明了具有平凡中心的限制李Rinehart代数能够分解成不可分解p-理想的直和,而且这种分解在不计p-理想次序的条件下是唯一的.
It is proved that restricted Lie-Rinehart algebras with trivial center can be decomposed into direct sum of indecomposable p-ideals and this decomposition is unique up to the order of the p-ideals.
It is proved that restricted Lie-Rinehart algebras with trivial center can be decomposed into direct sum of indecomposable p-ideals and this decomposition is unique up to the order of the p-ideals.
引文
[1]CASAS J.Obstructions to Lie-Rinehart algebra extensions[J].Algebra Colloq,2011,18:83-104.
[2]CASAS J,LADRA M,PIRASHVILI T.Crossed modules for Lie-Rinehart algebras[J].J Algebra,2004,274:192-201.
[3]CHEN L,ZHANG Y,MENG D.On the decomposition of restricted Lie superalgebras[J].Acta Math Sci,2007,27(A):577-583.
[4]CHEN Z,LIU Z,ZHONG D.Lie-Rinehart bialgebras for crossed products[J].J Pure Appl Algebra,2011,215:1270-1283.
[5]DOKAS I.Cohomology of restricted Lie-Rinehart algebras and the Brauer group[J].Adv Math,2012,231:2573-2592.
[6]HELGE M.Chem classes and Lie-Rinehart algebras[J].Indag Math,2007,18(4):589-599.
[7]HERZ J.Pseudo-algèbras de Lie[J].C R Acad Sci,1953,236:1935-1937.
[8]HUEBSCHMANN J.Extensions of Lie-Rinehart algebras and the Chern-Weil construction[J].Contemp Amer Math Soc,1999,227:145-176.
[9]HUEBSCHMANN J.Poisson cohomology and quantization[J].Reine Angew Math,1990,408:57-113.
[10]SUN B,CHEN L.Restricted and quasi-toral restricted Lie-Rinehart algebras[J].Open Math,2015,13(1):518-527.
[11]TOMASZ M.A pairing between super Lie-Rinehart and periodic cyclic homology[J].Commun Math Phys,2006,263(3):737-747.
[2]CASAS J,LADRA M,PIRASHVILI T.Crossed modules for Lie-Rinehart algebras[J].J Algebra,2004,274:192-201.
[3]CHEN L,ZHANG Y,MENG D.On the decomposition of restricted Lie superalgebras[J].Acta Math Sci,2007,27(A):577-583.
[4]CHEN Z,LIU Z,ZHONG D.Lie-Rinehart bialgebras for crossed products[J].J Pure Appl Algebra,2011,215:1270-1283.
[5]DOKAS I.Cohomology of restricted Lie-Rinehart algebras and the Brauer group[J].Adv Math,2012,231:2573-2592.
[6]HELGE M.Chem classes and Lie-Rinehart algebras[J].Indag Math,2007,18(4):589-599.
[7]HERZ J.Pseudo-algèbras de Lie[J].C R Acad Sci,1953,236:1935-1937.
[8]HUEBSCHMANN J.Extensions of Lie-Rinehart algebras and the Chern-Weil construction[J].Contemp Amer Math Soc,1999,227:145-176.
[9]HUEBSCHMANN J.Poisson cohomology and quantization[J].Reine Angew Math,1990,408:57-113.
[10]SUN B,CHEN L.Restricted and quasi-toral restricted Lie-Rinehart algebras[J].Open Math,2015,13(1):518-527.
[11]TOMASZ M.A pairing between super Lie-Rinehart and periodic cyclic homology[J].Commun Math Phys,2006,263(3):737-747.