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Nonlinear generalized Lie derivations on completely distributive commutative subspace lattice algebras
- Acta Scientiarum Naturalium Universitatis Sunyatseni Vol. 61, Issue 4, Pages: 170-177(2022)
- 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：
- 基金信息：
DOI：10.13471/j.cnki.acta.snus.2020A029
CLC： O177.2Published：25 July 2022，
Published Online：07 January 2022，
Received：01 July 2020，
Accepted：18 May 2021
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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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.
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