The decomposition of matrices corresponding to the 2-qutrit logic gate by succes-sive Cartan decomposition is investigated, and written in an exponential form based on the relationship between Lie group and Lie algebr...The decomposition of matrices corresponding to the 2-qutrit logic gate by succes-sive Cartan decomposition is investigated, and written in an exponential form based on the relationship between Lie group and Lie algebra, thus making them able to relate with the control field and the Hamiltonian of the system to perform the gate. Finally the decomposition of the ternary SWAP gate is presented in detail.展开更多
It is proved that the exact Borel subalgebras of a basic quasi-hereditary algebra are conjugate to each other. Moreover, the inner automorphism group of a basic quasi-hereditary algebra acts transitively on the set of...It is proved that the exact Borel subalgebras of a basic quasi-hereditary algebra are conjugate to each other. Moreover, the inner automorphism group of a basic quasi-hereditary algebra acts transitively on the set of its exact Borel subalgebras.展开更多
Characterizations of hereditary subalgebras generated by subsets of a C*-algebra are given through open projections.Using these results,we give some equivalent conditions of comparison of positive elements.
In this paper, we mainly study some properties of elementary n-Lie algebras, and prove some necessary and sufficient conditions for elementary n-Lie algebras. We also give the relations between elementary n-algebras a...In this paper, we mainly study some properties of elementary n-Lie algebras, and prove some necessary and sufficient conditions for elementary n-Lie algebras. We also give the relations between elementary n-algebras and E-algebras.展开更多
In this paper, we prove the nonimbedding theorem in nilpotent n-Lie algebras which is an analogue to the nonimbedding theorem of Burnsids in groups of prime power order. We also study the properties of Frattini subalg...In this paper, we prove the nonimbedding theorem in nilpotent n-Lie algebras which is an analogue to the nonimbedding theorem of Burnsids in groups of prime power order. We also study the properties of Frattini subalgebras of n-Lie algebras over the field with characteristic zero, and prove that the Frattini subalgebra of any k-solvable （k ≥2） n-Lie algebra is zero.展开更多
Let A be a quasi-hereditary algebra with a strong exact Borel subalgebra. It is proved that for any standard semisimple subalgebra T there exists an exact Borel subalgebra B of A such that T is a maximal semisimple su...Let A be a quasi-hereditary algebra with a strong exact Borel subalgebra. It is proved that for any standard semisimple subalgebra T there exists an exact Borel subalgebra B of A such that T is a maximal semisimple subalgebra of B. It is shown that the maximal length of flags of exact Borel subalgebras of A is the difference of the radium and the rank of Grothendic group of A plus 2. The number of conjugation-classes of exact Borel subalgebras is 1 if and only if A is basic; the number is 2 if and only if A is semisimple. For all other cases, this number is 0 or no less than 3. Furthermore, it is shown that all the exact Borel subalgebras are idempotent-conjugate to each other, that is, for any exact Borel subalgebras B and C of A, there exists an idempotent e of A, and an invertible element u of A, such that eBe = u-1eCeu.展开更多
In this paper,a new infinite-dimensional necklace Lie algebra is studied and the left and right index arrays of a necklace word in necklace Lie algebra is first defined.Using the left and right index arrays,we divide ...In this paper,a new infinite-dimensional necklace Lie algebra is studied and the left and right index arrays of a necklace word in necklace Lie algebra is first defined.Using the left and right index arrays,we divide the necklace words into 5 classes.We discuss finite-dimensional Lie subalgebras of necklace Lie algebras intensively and prove that some subalgebras are isomorphism to simple Lie algebra sl(n).展开更多
A Lie algebra endowed with a nondegenerate, symmetric, invariant bilinear form is called a quadratic Lie algebra. In this paper, the author investigates the structure of solvable quadratic Lie algebras, in particular,...A Lie algebra endowed with a nondegenerate, symmetric, invariant bilinear form is called a quadratic Lie algebra. In this paper, the author investigates the structure of solvable quadratic Lie algebras, in particular, the solvable quadratic Lie algebras whose Cartan subalgebras consist of semi-simple elements, the author presents a procedure to construct a class of quadratic Lie algebras from the point of view of cohomology and shows that all solvable quadratic Lie algebras can be obtained in this way.展开更多
基金the National Natural Science Foundation of China (Grant No. 60433050)the Key Project of the Science Foundation of Xuzhou Normal University, China (Grant No. 06XLA05)
文摘The decomposition of matrices corresponding to the 2-qutrit logic gate by succes-sive Cartan decomposition is investigated, and written in an exponential form based on the relationship between Lie group and Lie algebra, thus making them able to relate with the control field and the Hamiltonian of the system to perform the gate. Finally the decomposition of the ternary SWAP gate is presented in detail.
基金Project supported by the National Natural Science Foundation of China (Grant No. 19771070)partly supported by the NSF of Hainan Province (Grant No. 19702)by the Natural Science Foundation of Education Department of Hainan Province
文摘It is proved that the exact Borel subalgebras of a basic quasi-hereditary algebra are conjugate to each other. Moreover, the inner automorphism group of a basic quasi-hereditary algebra acts transitively on the set of its exact Borel subalgebras.
基金supported by National Natural Science Foundation of China(Grant No.10626031)Natural Science Foundation of Shandong Province (Grant No.Y2006A03)the Scientific Research Project of the Department of Education of Shandong Province (Grant No.J08LI15)
文摘Characterizations of hereditary subalgebras generated by subsets of a C*-algebra are given through open projections.Using these results,we give some equivalent conditions of comparison of positive elements.
基金The NSF(A2007000138,2005000088)of Hebei Provincethe NSF(y2004034)of Hebei University
文摘In this paper, we mainly study some properties of elementary n-Lie algebras, and prove some necessary and sufficient conditions for elementary n-Lie algebras. We also give the relations between elementary n-algebras and E-algebras.
基金The NSF(2005000088)of Hebei Province the NSF(y2004034)of Hebei University.
文摘In this paper, we prove the nonimbedding theorem in nilpotent n-Lie algebras which is an analogue to the nonimbedding theorem of Burnsids in groups of prime power order. We also study the properties of Frattini subalgebras of n-Lie algebras over the field with characteristic zero, and prove that the Frattini subalgebra of any k-solvable （k ≥2） n-Lie algebra is zero.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 10071062) also by the Doctorate Foundation of Hainan University and the Science and Technology Foundation of the Shanghai Jiaotong University.
文摘Let A be a quasi-hereditary algebra with a strong exact Borel subalgebra. It is proved that for any standard semisimple subalgebra T there exists an exact Borel subalgebra B of A such that T is a maximal semisimple subalgebra of B. It is shown that the maximal length of flags of exact Borel subalgebras of A is the difference of the radium and the rank of Grothendic group of A plus 2. The number of conjugation-classes of exact Borel subalgebras is 1 if and only if A is basic; the number is 2 if and only if A is semisimple. For all other cases, this number is 0 or no less than 3. Furthermore, it is shown that all the exact Borel subalgebras are idempotent-conjugate to each other, that is, for any exact Borel subalgebras B and C of A, there exists an idempotent e of A, and an invertible element u of A, such that eBe = u-1eCeu.
文摘In this paper,a new infinite-dimensional necklace Lie algebra is studied and the left and right index arrays of a necklace word in necklace Lie algebra is first defined.Using the left and right index arrays,we divide the necklace words into 5 classes.We discuss finite-dimensional Lie subalgebras of necklace Lie algebras intensively and prove that some subalgebras are isomorphism to simple Lie algebra sl(n).
基金supported by the National Natural Science Foundation of China(Grant No.10571119)the Natural Science Funds from Morningside Center of Mathematics,Chinese Academy of Sciencesthe Eduction Department of Jiangsu Province.
文摘A Lie algebra endowed with a nondegenerate, symmetric, invariant bilinear form is called a quadratic Lie algebra. In this paper, the author investigates the structure of solvable quadratic Lie algebras, in particular, the solvable quadratic Lie algebras whose Cartan subalgebras consist of semi-simple elements, the author presents a procedure to construct a class of quadratic Lie algebras from the point of view of cohomology and shows that all solvable quadratic Lie algebras can be obtained in this way.
