完全分配可交换子空间格代数上的非线性广义Lie导子
Nonlinear generalized Lie derivations on completely distributive commutative subspace lattice algebras
- 中山大学学报(自然科学版)(中英文) 2022年61卷第4期 页码：170-177
- 作者机构：
1.咸阳师范学院数学与信息科学学院， 陕西 咸阳 712000
2.陕西师范大学数学与信息科学学院， 陕西 西安 710062
- 作者简介：
马飞（1981年生），男；研究方向：算子代数与自由概率；E-mail：mafei6337@sina.com
张建华（1965年生），男；研究方向：算子代数与自由概率；E-mail：jhzhang@snnu.edu.cn
- 基金信息：国家自然科学基金(11471199);陕西省教育厅研究计划项目(19JK0929);咸阳师范学院青蓝人才项目(XSYQL201801)
DOI：10.13471/j.cnki.acta.snus.2020A029
中图分类号： O177.2纸质出版日期：2022-07-25，
网络出版日期：2022-01-07，
收稿日期：2020-07-01，
录用日期：2021-05-18
扫 描 看 全 文
马飞,张建华,刘红哲.完全分配可交换子空间格代数上的非线性广义Lie导子[J].中山大学学报(自然科学版),2022,61(04):170-177.
MA Fei,ZHANG Jianhua,LIU Hongzhe.Nonlinear generalized Lie derivations on completely distributive commutative subspace lattice algebras[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2022,61(04):170-177.
马飞,张建华,刘红哲.完全分配可交换子空间格代数上的非线性广义Lie导子[J].中山大学学报(自然科学版),2022,61(04):170-177. DOI： 10.13471/j.cnki.acta.snus.2020A029.
MA Fei,ZHANG Jianhua,LIU Hongzhe.Nonlinear generalized Lie derivations on completely distributive commutative subspace lattice algebras[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2022,61(04):170-177. DOI： 10.13471/j.cnki.acta.snus.2020A029.
摘要
设
<math id="M1"><mi mathvariant="normal">A</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">ℒ</mi></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49452505&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49452502&type=
6.60400009
2.96333337
是 Hilbert 空间
<math id="M2"><mi mathvariant="normal">H</mi></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49452476&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49452473&type=
2.28600001
2.28600001
上的一个完全分配可交换子空间格代数，
<math id="M3"><mi>f</mi></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49452567&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49452559&type=
0.93133330
2.96333337
是
<math id="M4"><mi mathvariant="normal">A</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">ℒ</mi></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49452505&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49452502&type=
6.60400009
2.96333337
上的非线性广义Lie 导子，
<math id="M5"><mi>d</mi></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49452574&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49452570&type=
1.60866666
2.28600001
是
<math id="M6"><mi mathvariant="normal">A</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">ℒ</mi></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49452542&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49452539&type=
6.60400009
2.96333337
上与
<math id="M7"><mi>f</mi></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49452567&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49452559&type=
0.93133330
2.96333337
相关的非线性映射，则
<math id="M8"><mi>f</mi></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49452567&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49452559&type=
0.93133330
2.96333337
和
<math id="M9"><mi>d</mi></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49452574&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49452570&type=
1.60866666
2.28600001
分别是可加广义导子和交换子上为零的映射之和。
Abstract
Let
<math id="M10"><mi mathvariant="normal">A</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">ℒ</mi></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49452589&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49452585&type=
6.60400009
2.96333337
be a completely distributive commutative subspace lattice algebra，
<math id="M11"><mi>f</mi></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49452643&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49452626&type=
1.10066664
3.38666677
be a nonlinear generalized Lie derivation on
<math id="M12"><mi mathvariant="normal">A</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">ℒ</mi></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49452619&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49452602&type=
6.60400009
2.96333337
with an associated nonlinear map
<math id="M13"><mi>d</mi></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49452648&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49452645&type=
1.86266661
2.70933342
.Then
<math id="M14"><mi>f</mi></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49452643&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49452626&type=
1.10066664
3.38666677
and
<math id="M15"><mi>d</mi></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49452648&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49452645&type=
1.86266661
2.70933342
are the sum of an additive generalized derivation and a map into its center sending each commutator to zero，respectively.
关键词
完全分配可交换子空间格代数非线性广义Lie导子广义导子
Keywords
completely distributive commutative subspace lattice algebranonlinear generalized Lie derivationgeneralized derivation
references
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FEI X H， ZHANG J H. Nonlinear generalized Lie derivations on triangular algebras ［J］. Linear and Multilinear Algebra， 2017， 65（6）： 1158-1170.
LAMBROU M S. Complete distributivity lattices ［J］. Fundamental Math， 1983， 119（3）： 227-240.
马飞，张建华，贺雯．CDC-代数上的广义Jordan中心化子［J］．山东大学学报（理学版）， 2015， 50（6）： 83-88.
LAURIE C， LONGSTAFF W. A note on rank-one operators in reflexive algebras ［J］. Proc Amer Math Soc， 1983， 89（2）： 293-297.
GILFEATHER F， MOORE R L. Isomorphisms of certain CSL algebras ［J］. J Funct Anal， 2010， 67（2）： 264-291.
LU F Y. Lie derivations of certain CSL algebras ［J］. Israel J Math， 2006， 155（1）： 149-156.
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