Representations and module-extensions of 3-hom-Lie algebras

详细信息    查看全文

• 作者：Yan Liu^a ; Liangyun Chen^a ; ^{chenly640@nenu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Yao Ma^b
• 关键词：17A45 ; 17B30 ; 17B10
• 刊名：Journal of Geometry and Physics
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：98
• 期：Complete
• 页码：376-383
• 全文大小：398 K

文摘

In this paper, we study the representations and module-extensions of 3-hom-Lie algebras. We show that a linear map between 3-hom-Lie algebras is a morphism if and only if its graph is a hom subalgebra and show that the set of derivations of a 3-hom-Lie algebra is a Lie algebra. Moreover, we introduce the definition of mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0393044015002041&_mathId=si1.gif&_user=111111111&_pii=S0393044015002041&_rdoc=1&_issn=03930440&md5=4d81ad8e570ea1b18a0e417b388c6daa" title="Click to view the MathML source">T_θmathContainer hidden">mathCode"><math altimg="si1.gif" overflow="scroll">Tθmath>-extensions and mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0393044015002041&_mathId=si2.gif&_user=111111111&_pii=S0393044015002041&_rdoc=1&_issn=03930440&md5=a033bc73c355cdf78a2bddce1dac222c">mage" height="17" width="17" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0393044015002041-si2.gif">mathContainer hidden">mathCode"><math altimg="si2.gif" overflow="scroll">Tθ∗math>-extensions of 3-hom-Lie algebras in terms of modules, providing the necessary and sufficient conditions for a mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0393044015002041&_mathId=si3.gif&_user=111111111&_pii=S0393044015002041&_rdoc=1&_issn=03930440&md5=e22850e5f072646a246222dacd661d6f" title="Click to view the MathML source">2kmathContainer hidden">mathCode"><math altimg="si3.gif" overflow="scroll">2kmath>-dimensional metric 3-hom-Lie algebra to be isometric to a mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0393044015002041&_mathId=si2.gif&_user=111111111&_pii=S0393044015002041&_rdoc=1&_issn=03930440&md5=a033bc73c355cdf78a2bddce1dac222c">mage" height="17" width="17" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0393044015002041-si2.gif">mathContainer hidden">mathCode"><math altimg="si2.gif" overflow="scroll">Tθ∗math>-extension.