A characterization of finite dimensional nilpotent Filippov algebras

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• 作者：H. Darabi ^{darabi@iauesf.ac.ir" class="auth_mail" title="E-mail the corresponding author} ; F. Saeedi ; ^{saeedi@mshdiau.ac.ir" class="auth_mail" title="E-mail the corresponding author} ; M. Eshrati ^{eshrati.me@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 17B05 ; secondary ; 17B30
• 刊名：Journal of Geometry and Physics
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：101
• 期：Complete
• 页码：100-107
• 全文大小：385 K

文摘

Let an id="mmlsi23" class="mathmlsrc">an class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S039304401500282X&_mathId=si23.gif&_user=111111111&_pii=S039304401500282X&_rdoc=1&_issn=03930440&md5=ba5c6c2d01d6748500fab76a354a430e" title="Click to view the MathML source">Aan>an class="mathContainer hidden">an class="mathCode">ath altimg="si23.gif" overflow="scroll">Aath>an>an>an> be a nilpotent Filippov (an id="mmlsi24" class="mathmlsrc">an class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S039304401500282X&_mathId=si24.gif&_user=111111111&_pii=S039304401500282X&_rdoc=1&_issn=03930440&md5=23a3156f5ca5dc50d9322a09947a8569" title="Click to view the MathML source">nan>an class="mathContainer hidden">an class="mathCode">ath altimg="si24.gif" overflow="scroll">nath>an>an>an>-Lie) algebra of dimension an id="mmlsi25" class="mathmlsrc">an class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S039304401500282X&_mathId=si25.gif&_user=111111111&_pii=S039304401500282X&_rdoc=1&_issn=03930440&md5=84fdfc7630ac7824978bd00cc7cd49ae" title="Click to view the MathML source">dan>an class="mathContainer hidden">an class="mathCode">ath altimg="si25.gif" overflow="scroll">dath>an>an>an> and put an id="mmlsi26" class="mathmlsrc"><a title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S039304401500282X&_mathId=si26.gif&_user=111111111&_pii=S039304401500282X&_rdoc=1&_issn=03930440&md5=5d5db67a2b07284ab5bd3d546721121e">ass="imgLazyJSB inlineImage" height="23" width="228" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S039304401500282X-si26.gif">a>an class="mathContainer hidden">an class="mathCode">ath altimg="si26.gif" overflow="scroll">s(A)=(ac linethickness="00">d−1nac>)+n−1−dimathvariant="script">M(A)ath>an>an>an> and an id="mmlsi27" class="mathmlsrc"><a title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S039304401500282X&_mathId=si27.gif&_user=111111111&_pii=S039304401500282X&_rdoc=1&_issn=03930440&md5=2650cbd3251bc965440328e860c00f5e">ass="imgLazyJSB inlineImage" height="23" width="156" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S039304401500282X-si27.gif">a>an class="mathContainer hidden">an class="mathCode">ath altimg="si27.gif" overflow="scroll">t(A)=(ac linethickness="00">dnac>)−dimathvariant="script">M(A)ath>an>an>an>, where an id="mmlsi28" class="mathmlsrc">an class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S039304401500282X&_mathId=si28.gif&_user=111111111&_pii=S039304401500282X&_rdoc=1&_issn=03930440&md5=c650229a53be72b1079d80d809f1f385" title="Click to view the MathML source">M(A)an>an class="mathContainer hidden">an class="mathCode">ath altimg="si28.gif" overflow="scroll">athvariant="script">M(A)ath>an>an>an> denotes the multiplier of an id="mmlsi23" class="mathmlsrc">an class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S039304401500282X&_mathId=si23.gif&_user=111111111&_pii=S039304401500282X&_rdoc=1&_issn=03930440&md5=ba5c6c2d01d6748500fab76a354a430e" title="Click to view the MathML source">Aan>an class="mathContainer hidden">an class="mathCode">ath altimg="si23.gif" overflow="scroll">Aath>an>an>an>. The aim of this paper is to classify all nilpotent an id="mmlsi24" class="mathmlsrc">an class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S039304401500282X&_mathId=si24.gif&_user=111111111&_pii=S039304401500282X&_rdoc=1&_issn=03930440&md5=23a3156f5ca5dc50d9322a09947a8569" title="Click to view the MathML source">nan>an class="mathContainer hidden">an class="mathCode">ath altimg="si24.gif" overflow="scroll">nath>an>an>an>-Lie algebras an id="mmlsi23" class="mathmlsrc">an class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S039304401500282X&_mathId=si23.gif&_user=111111111&_pii=S039304401500282X&_rdoc=1&_issn=03930440&md5=ba5c6c2d01d6748500fab76a354a430e" title="Click to view the MathML source">Aan>an class="mathContainer hidden">an class="mathCode">ath altimg="si23.gif" overflow="scroll">Aath>an>an>an> for which an id="mmlsi32" class="mathmlsrc">an class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S039304401500282X&_mathId=si32.gif&_user=111111111&_pii=S039304401500282X&_rdoc=1&_issn=03930440&md5=4d3b6972f8bccf9424e86729ceb9cbe2" title="Click to view the MathML source">s(A)=0an>an class="mathContainer hidden">an class="mathCode">ath altimg="si32.gif" overflow="scroll">s(A)=0ath>an>an>an>, 1 or 2, and apply it in order to determine all nilpotent an id="mmlsi24" class="mathmlsrc">an class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S039304401500282X&_mathId=si24.gif&_user=111111111&_pii=S039304401500282X&_rdoc=1&_issn=03930440&md5=23a3156f5ca5dc50d9322a09947a8569" title="Click to view the MathML source">nan>an class="mathContainer hidden">an class="mathCode">ath altimg="si24.gif" overflow="scroll">nath>an>an>an>-Lie algebras an id="mmlsi23" class="mathmlsrc">an class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S039304401500282X&_mathId=si23.gif&_user=111111111&_pii=S039304401500282X&_rdoc=1&_issn=03930440&md5=ba5c6c2d01d6748500fab76a354a430e" title="Click to view the MathML source">Aan>an class="mathContainer hidden">an class="mathCode">ath altimg="si23.gif" overflow="scroll">Aath>an>an>an> satisfying an id="mmlsi35" class="mathmlsrc">an class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S039304401500282X&_mathId=si35.gif&_user=111111111&_pii=S039304401500282X&_rdoc=1&_issn=03930440&md5=cc3f92ea6f699fecfadc3e31271a8841" title="Click to view the MathML source">0≤t(A)≤8an>an class="mathContainer hidden">an class="mathCode">ath altimg="si35.gif" overflow="scroll">0≤t(A)≤8ath>an>an>an>.