We introduce elementary and Ф-free Lie triple systems and study the properties of these systems. In particular, structures of subsystems of an elementary Lie triple system and a class of Ф-free Lie triple systems ar...We introduce elementary and Ф-free Lie triple systems and study the properties of these systems. In particular, structures of subsystems of an elementary Lie triple system and a class of Ф-free Lie triple systems are investigated.展开更多
We study the Banach-Lie group Ltaut（A） of Lie triple automorphisms of a complex associative H^＊-algebra A. Some consequences about its Lie algebra, the algebra of Lie triple derivations of A, Ltder（A）, are obtain...We study the Banach-Lie group Ltaut（A） of Lie triple automorphisms of a complex associative H^＊-algebra A. Some consequences about its Lie algebra, the algebra of Lie triple derivations of A, Ltder（A）, are obtained. For a topologically simple A, in the infinite-dimensional case we have Ltaut（A）0 = Aut（A） implying Ltder（A） = Der（A）. In the finite-dimensional case Ltaut（A）0 is a direct product of Aut（A） and a certain subgroup of Lie derivations δ from A to its center, annihilating commutators.展开更多
For a Lie triple system T over a field of characteristic zero, some sufficient conditions for T to be two-generated are proved. We also discuss to what extent the two-generated subsystems determine the structure of th...For a Lie triple system T over a field of characteristic zero, some sufficient conditions for T to be two-generated are proved. We also discuss to what extent the two-generated subsystems determine the structure of the system T . One of the main results is that T is solvable if and only if every two elements generates a solvable subsystem. In fact, we give an explicit two-generated law for the two-generated subsystems.展开更多
In this paper, we mainly concerned about the nilpotence of Lie triple algebras.We give the definition of nilpotence of the Lie triple algebra and obtained that if Lie triplealgebra is nilpotent, then its standard enve...In this paper, we mainly concerned about the nilpotence of Lie triple algebras.We give the definition of nilpotence of the Lie triple algebra and obtained that if Lie triplealgebra is nilpotent, then its standard enveloping Lie algebra is nilpotent.展开更多
In addressing the challenge of motion artifacts in Positron Emission Tomography (PET) lung scans, our studyintroduces the Triple Equivariant Motion Transformer (TEMT), an innovative, unsupervised, deep-learningbasedfr...In addressing the challenge of motion artifacts in Positron Emission Tomography (PET) lung scans, our studyintroduces the Triple Equivariant Motion Transformer (TEMT), an innovative, unsupervised, deep-learningbasedframework for efficient respiratory motion correction in PET imaging. Unlike traditional techniques,which segment PET data into bins throughout a respiratory cycle and often face issues such as inefficiency andoveremphasis on certain artifacts, TEMT employs Convolutional Neural Networks (CNNs) for effective featureextraction and motion decomposition.TEMT’s unique approach involves transforming motion sequences into Liegroup domains to highlight fundamental motion patterns, coupled with employing competitive weighting forprecise target deformation field generation. Our empirical evaluations confirm TEMT’s superior performancein handling diverse PET lung datasets compared to existing image registration networks. Experimental resultsdemonstrate that TEMT achieved Dice indices of 91.40%, 85.41%, 79.78%, and 72.16% on simulated geometricphantom data, lung voxel phantom data, cardiopulmonary voxel phantom data, and clinical data, respectively. Tofacilitate further research and practical application, the TEMT framework, along with its implementation detailsand part of the simulation data, is made publicly accessible at https://github.com/yehaowei/temt.展开更多
Let A be a factor. For A, B ∈4, define by [A, B]. = AB- BA＊ the skew Lie product of A and B. In this article, it is proved that a map φ： A- A satisfies φ（[[A, B]., C].） = [[φ（A）, B]., C]. ＋ [[A, φ（B）]. C...Let A be a factor. For A, B ∈4, define by [A, B]. = AB- BA＊ the skew Lie product of A and B. In this article, it is proved that a map φ： A- A satisfies φ（[[A, B]., C].） = [[φ（A）, B]., C]. ＋ [[A, φ（B）]. C]. ＋ [[A, B]., φ（C）]. for all A, B, C∈ A if and only if φ is an additive ＊-derivation.展开更多
In the present paper, we develop initially the Frattini theory for Lie supertriple systems, obtain some properties of the Frattini subsystem and show that the intersection of all maximal subsystems of a solvable Lie s...In the present paper, we develop initially the Frattini theory for Lie supertriple systems, obtain some properties of the Frattini subsystem and show that the intersection of all maximal subsystems of a solvable Lie supertriple system is its ideal. Moreover, we give the relationship between φ-free and complemented for Lie supertriple system.展开更多
As a natural generalization of a restricted Lie algebra, a restricted Lie triple system was defined by Hodge. In this paper, we develop initially the Frattini theory for restricted Lie triple systems, generalize some ...As a natural generalization of a restricted Lie algebra, a restricted Lie triple system was defined by Hodge. In this paper, we develop initially the Frattini theory for restricted Lie triple systems, generalize some results of Frattini p-subalgebra for restricted Lie algebras, obtain some properties of the Frattini p-subsystem and give the relationship between Фp（T） and Ф（T） for solvable Lie triple systems.展开更多
Let T（n, R） be the Lie algebra consisting of all n× n upper triangular matrices over a commutative ring R with identity 1 and M be a 2-torsion free unital T（n, R）-bimodule. In this paper, we prove that every ...Let T（n, R） be the Lie algebra consisting of all n× n upper triangular matrices over a commutative ring R with identity 1 and M be a 2-torsion free unital T（n, R）-bimodule. In this paper, we prove that every Lie triple derivation d ： T（n, R） →M is the sum of a Jordan derivation and a central Lie triple derivation.展开更多
基金supported in part by the National Natural Science Foundation of China(10871192)NSF(A2010000194) of Hebei Province,China
文摘We introduce elementary and Ф-free Lie triple systems and study the properties of these systems. In particular, structures of subsystems of an elementary Lie triple system and a class of Ф-free Lie triple systems are investigated.
基金Supported by the PCI of the UCA ‘Teoría de Lie y Teoría de Espacios de Banachthe PAI with project numbers FQM-298 and FQM-336the project of the Spanish Ministerio de Educación y Ciencia MTM2004-06580-C02-02 and with fondos FEDER
文摘We study the Banach-Lie group Ltaut（A） of Lie triple automorphisms of a complex associative H^＊-algebra A. Some consequences about its Lie algebra, the algebra of Lie triple derivations of A, Ltder（A）, are obtained. For a topologically simple A, in the infinite-dimensional case we have Ltaut（A）0 = Aut（A） implying Ltder（A） = Der（A）. In the finite-dimensional case Ltaut（A）0 is a direct product of Aut（A） and a certain subgroup of Lie derivations δ from A to its center, annihilating commutators.
文摘For a Lie triple system T over a field of characteristic zero, some sufficient conditions for T to be two-generated are proved. We also discuss to what extent the two-generated subsystems determine the structure of the system T . One of the main results is that T is solvable if and only if every two elements generates a solvable subsystem. In fact, we give an explicit two-generated law for the two-generated subsystems.
基金Supported by NKBRPC(2004CB31800)Supported by NNSFC(10375087)
文摘In this paper, we mainly concerned about the nilpotence of Lie triple algebras.We give the definition of nilpotence of the Lie triple algebra and obtained that if Lie triplealgebra is nilpotent, then its standard enveloping Lie algebra is nilpotent.
基金the National Natural Science Foundation of China(No.82160347)Yunnan Provincial Science and Technology Department(No.202102AE090031)Yunnan Key Laboratory of Smart City in Cyberspace Security(No.202105AG070010).
文摘In addressing the challenge of motion artifacts in Positron Emission Tomography (PET) lung scans, our studyintroduces the Triple Equivariant Motion Transformer (TEMT), an innovative, unsupervised, deep-learningbasedframework for efficient respiratory motion correction in PET imaging. Unlike traditional techniques,which segment PET data into bins throughout a respiratory cycle and often face issues such as inefficiency andoveremphasis on certain artifacts, TEMT employs Convolutional Neural Networks (CNNs) for effective featureextraction and motion decomposition.TEMT’s unique approach involves transforming motion sequences into Liegroup domains to highlight fundamental motion patterns, coupled with employing competitive weighting forprecise target deformation field generation. Our empirical evaluations confirm TEMT’s superior performancein handling diverse PET lung datasets compared to existing image registration networks. Experimental resultsdemonstrate that TEMT achieved Dice indices of 91.40%, 85.41%, 79.78%, and 72.16% on simulated geometricphantom data, lung voxel phantom data, cardiopulmonary voxel phantom data, and clinical data, respectively. Tofacilitate further research and practical application, the TEMT framework, along with its implementation detailsand part of the simulation data, is made publicly accessible at https://github.com/yehaowei/temt.
基金Supported by National Natural Science Foundation of China(Grant Nos.11526123,11401273)the Natural Science Foundation of Shandong Province,China(Grant No.ZR2015PA010)
文摘Let A be a factor. For A, B ∈4, define by [A, B]. = AB- BA＊ the skew Lie product of A and B. In this article, it is proved that a map φ： A- A satisfies φ（[[A, B]., C].） = [[φ（A）, B]., C]. ＋ [[A, φ（B）]. C]. ＋ [[A, B]., φ（C）]. for all A, B, C∈ A if and only if φ is an additive ＊-derivation.
基金Supported by the National Natural Science Foundation of China (Grant Nos. 10701019 10871057)
文摘In the present paper, we develop initially the Frattini theory for Lie supertriple systems, obtain some properties of the Frattini subsystem and show that the intersection of all maximal subsystems of a solvable Lie supertriple system is its ideal. Moreover, we give the relationship between φ-free and complemented for Lie supertriple system.
基金Supported by National Natural Science Foundation of China (Grant Nos. 10701019 and 10871057)the Fundamental Research Funds for the Central Universities, the ZJZSF (Grant Nos. Y607136, D7080080)+1 种基金Qianjiang Excellence Project (Grant No. 2007R10031)the New Century 151 Talent Project (2008) of Zhejiang Province
文摘As a natural generalization of a restricted Lie algebra, a restricted Lie triple system was defined by Hodge. In this paper, we develop initially the Frattini theory for restricted Lie triple systems, generalize some results of Frattini p-subalgebra for restricted Lie algebras, obtain some properties of the Frattini p-subsystem and give the relationship between Фp（T） and Ф（T） for solvable Lie triple systems.
基金Supported by the National Natural Science Foundation of China (Grant No. 10771027)
文摘Let T（n, R） be the Lie algebra consisting of all n× n upper triangular matrices over a commutative ring R with identity 1 and M be a 2-torsion free unital T（n, R）-bimodule. In this paper, we prove that every Lie triple derivation d ： T（n, R） →M is the sum of a Jordan derivation and a central Lie triple derivation.
