On the structure of graded Leibniz triple systems
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- 作者：Yan Caoa ; b ; Liangyun Chena ; chenly640@nenu.edu.cn" class="auth_mail" title="E-mail the corresponding author
- 关键词：17A32 ; 17A60 ; 17B22 ; 17B65
- 刊名：Linear Algebra and its Applications
- 出版年：2016
- 出版时间：1 May 2016
- 年：2016
- 卷：496
- 期：Complete
- 页码：496-509
- 全文大小：344 K
文摘
We study the structure of a Leibniz triple system mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516000859&_mathId=si1.gif&_user=111111111&_pii=S0024379516000859&_rdoc=1&_issn=00243795&md5=1c12ad5d547458cdc12d6fdb8eae3edb" title="Click to view the MathML source">EmathContainer hidden">mathCode"><math altimg="si1.gif" overflow="scroll">mathvariant="script">E math> graded by an arbitrary abelian group G which is considered of arbitrary dimension and over an arbitrary base field mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516000859&_mathId=si2.gif&_user=111111111&_pii=S0024379516000859&_rdoc=1&_issn=00243795&md5=c93da194dc5556eb25fedad54f6384fa" title="Click to view the MathML source">KmathContainer hidden">mathCode"><math altimg="si2.gif" overflow="scroll">mathvariant="double-struck">K math>. We show that mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516000859&_mathId=si1.gif&_user=111111111&_pii=S0024379516000859&_rdoc=1&_issn=00243795&md5=1c12ad5d547458cdc12d6fdb8eae3edb" title="Click to view the MathML source">EmathContainer hidden">mathCode"><math altimg="si1.gif" overflow="scroll">mathvariant="script">E math> is of the form mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516000859&_mathId=si10.gif&_user=111111111&_pii=S0024379516000859&_rdoc=1&_issn=00243795&md5=897a6ebbc57fdbc9d92c9f0e17d8e331" title="Click to view the MathML source">E=U+∑[j]∈∑1/∼I[j]mathContainer hidden">mathCode"><math altimg="si10.gif" overflow="scroll">mathvariant="script">E = U + ∑ [ j ] ∈ ∑ 1 / ∼ I [ j ] mathvariant="script">E 1 I [ j ] mathvariant="script">E math>, satisfying mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516000859&_mathId=si6.gif&_user=111111111&_pii=S0024379516000859&_rdoc=1&_issn=00243795&md5=e577460bf4d76059fafbaab15011e96b" title="Click to view the MathML source">{I[j],E,I[k]}={I[j],I[k],E}={E,I[j],I[k]}=0mathContainer hidden">mathCode"><math altimg="si6.gif" overflow="scroll">{ I [ j ] , mathvariant="script">E , I [ k ] } = { I [ j ] , I [ k ] , mathvariant="script">E } = { mathvariant="script">E , I [ j ] , I [ k ] } = 0 math> if mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516000859&_mathId=si7.gif&_user=111111111&_pii=S0024379516000859&_rdoc=1&_issn=00243795&md5=4f58c767b88f8db9163a28eb0e5359c5" title="Click to view the MathML source">[j]≠[k]mathContainer hidden">mathCode"><math altimg="si7.gif" overflow="scroll">[ j ] ≠ [ k ] math>, where the relation ∼ in mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516000859&_mathId=si8.gif&_user=111111111&_pii=S0024379516000859&_rdoc=1&_issn=00243795&md5=d9288507edee4e9c3c71eeeef15eb8f4" title="Click to view the MathML source">∑1={g∈G∖{1}:Lg≠0}mathContainer hidden">mathCode"><math altimg="si8.gif" overflow="scroll">∑ 1 = { g ∈ G ∖ { 1 } : L g ≠ 0 } math>, defined by mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516000859&_mathId=si12.gif&_user=111111111&_pii=S0024379516000859&_rdoc=1&_issn=00243795&md5=eb283d1d7dbff02277f74b0db5dcecbe" title="Click to view the MathML source">g∼hmathContainer hidden">mathCode"><math altimg="si12.gif" overflow="scroll">g ∼ h math> if and only if g is connected to h.