查询词典 operator algebra

The thesis studies the formation of several basic algebraic terms such as "algebra","equation" in the book of Elements of Algebra and Algebra.

本文的研究表明，术语与其所表述的数学内容之间的差异反映当时数学术语在翻译时不能保证单义性和系统性。

Weak quasi-bialgebra (quasi-Ilopf algebra) is an associative algebra with unit 1 a non-unital algebra map i.

弱拟双代数是一个具有单位1的结合代数，具有余乘法与余单位。

Firstly,a involution on Universal Clifford algebra 〓 is introduced.then we equip a inner product and the corresponding two equivalent norms onUniversal Clifford algebra 〓,and then we prove that Universal Cliffordalgebra 〓 is a Banach algebra with one of the above norms,these resultsare very important for further study in this field.

第一，本文创造性地准确地给出了在少Clifford代数〓上的一个对合运算表示，由此，我们给出了在泛Clifford代数〓上的一个内积，然后给出了相应的在泛Clifford代数〓上的两个等价的范数，并证明了若在〓上赋予其中的一个范数，则〓是一个Banach代数，这为在泛Clifford分析中进一步开展工作奠定了初步的基础。

Next, we discuss the relations between left quasi-dual bimodules and left dual-bimodules, we obtain that a left quasi-dual bimodule is a left dual bimodule if it satisfies one of the following conditions: sM is minimal injective and MR is a M-minimal injective kasch-module; MR is a M-minimal injective kasch-module and for any two ideals LI and L2 ofSS rM(L1 n L2)-rw(L1)+rM(I2); sM is minimal injective and for any two submodules A and B of MR,Lastly, we applicate the quasi-duality on smash product algebra R#H, and obtain an answer of the semiprime problem, i.e., let H be a finite-dimensional semisimple Hopf algebra and R be an H-module algebra, if R is left quasi-dual and semiprime, then R#H is semiprime.

我们得到：一个左拟对偶双边模如果满足下列条件之一，则它将成为一个左对偶双边模：_sM是单内射的并且M_R是一个M-单内射kasch-模；M_R是一个M-单内射kasch-模并且对_sS的任意两个理想，有r_M(L_1∩L_2)=r_M(L_1)+r_M(L_2)；_sM是单内射的且对M_R的任意两个子模，有l_s=l_s+l_s。2 在第2.3节中我们将拟对偶性应用于smash积代数R#H，部分解决了半素问题。

Theorem C: The commutator algebra of so *(2 n ) is its own, and the commutator algebra ofand the commutator algebra of Theorem D: The Cartan subalgebra ofand the Cartan subalgebra of Theorem E: The structural formula of

定理C so *(2 n )的换位子代数就是其本身， g *(2 n， S ， C )的换位子代数为g *(2 n + 1， S ， C)的换位子代数为定理D so *(2 n )和g *(2 n ， S ， C )的Cartan子代数是定理E so *(2 n )和g * m， S ，(来源：AB78C论文网www.abclunwen.comC 的结构公式都是来源：A6bBCe9论文网www.abclunwen.com

Ringel has given and studied the N_0I-graded twisted coalgebra and Ringel-Hall algebra in the reference [1]. Subsequently, people found that there is an analogy between Ringel-Hall algebra and Hopf algebra, and then they introduced the concept of twisted Hopf algebras and bitwisted Hopf algebras, and worked on them.

Ringel在[1]中引入并研究了N_0I-分次扭的余代数和Ringel-Hall代数，后来人们发现Ringel-Hall代数有类似Hopf代数的结构，随后，扭Hopf代数、双扭Hopf代数先后被引入和研究。

In chapter 5, local derivations and local automorphisms of nest subalgebras in von Neumann algebras and local higher cohomology -local 2-cocycles are studied. It is proved that every weakly continuous local derivation, respectively, every weakly local automorphism, of nest subalgebra of a factor von Neumann algebra is a derivation, respectively, an automorphism. Every norm continuous local derivation, respectively, every norm local automorphism, of the nest subalgebra associated to a countable nest in a factor von Neumann algebra is a derivation, respectively, an automorphism. Moreover, it is answered Larson's question. Finally, it is shown that every local 2-cocycle of any von Neumann algebra is a 2-cocycle.

第五章研究von Neumann代数中套子代数的局部导子和局部同构以及von Neumann代数的高维局部映射—局部2-上循环，证明了因子von Neumann代数中套子代数的每一个局部强连续导子和局部强连续同构分别是导子和同构；可数套所对应的套子代数的每一个有界局部导子和有界局部同构分别是导子和同构；同时，部分回答了Larson所提的问题；最后，得到von Neumann代数的每一个局部2-上循环是2-上循环。

Put forward a commutative law in the weak fuzzy implication algebra;The properties of weak FI-algebra and FI-algebra are studied.

引入可交换弱FI代数的概念，讨论了弱FI代数和FI代数的几个性质；进一步得到了交换弱FI代数和交换FI代数的一些结果。

We showthat End〓is an algebra in 〓,and then we construct a derived Lie algebra〓 in 〓 and prove existenceness of its enveloping algebra under the condi-tion that the"braiding"in the category 〓 is symmetric on 〓.

Radford的双积定理给出了在Yetter-Drinfel'd范畴〓中构造辫子群[48-50]的一种方法。因为，冲积已被发展为交叉积，许多冲积的相应结果被搬到了交叉积上。

The research of differential structure on the algebra system, has opened up a new field for the research of algebra, and offered a new method and thinking, greatly expanded the scope of application of algebra.

代数系统上的微分结构的研究，为代数学的研究开辟了新的领域，提供了新的方法和思路，极大的扩展了代数学应用的范围。

"Yes, now you can give yourself airs," she said, you have got what you wanted.

"对了，您现在高兴了，"她说道，这是您所期待的。

Then the LORD said to me: Rebel Israel is inwardly more just than traitorous Judah.

上主于是对我说：＂失节的以色列比失信的犹大，更显得正义。