共查询到18条相似文献,搜索用时 54 毫秒
1.
张伦传 《应用泛函分析学报》2003,5(3):210-212
获得了Hilbert C^*-模之间的两个同构定理.作为推论,证明了C^*-代数上每个可数生成的Hilbert C^*-模均稳定酉等价于A。 相似文献
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假设G是一个p-可解群,A是一个可解群,它作用在G上且它的阶与G的阶互素,对适当的Dedekind整环R和RG的一个块B,A平凡地作用在它的某一个亏群上,我们证明B与它的Watanabe对应之间存在一个Morita等价. 相似文献
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设S,R是可分解半群.记US-FAct={sM∈S-Act|SM=M且SHoms(S,M)≌M],给出了范畴US-FAct与UR-FAct等价的刻划;S分别强Morita等价于一个夹层半群、局部单位半群、幺半群和群的条件;S是完全单半群当且仅当S强Morita等价于一个群且对任何指标集I,S SHoms(S,i∈I S)→i∈I S,s t·f→(st)f,是同构. 相似文献
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给出了弱Hopf代数上的Maschke定理, 推广了由Cohen和Fishman给出的著名的Maschke定理, 并且在弱Hopf代数上构造了 Morita关系. 相似文献
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在Hilbert C~*-模框架下,给出了闭子模之间的酉等价与相应的遗传C~*-子代数的*同构,及对应的开投影的等价性的关系定理. 相似文献
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设 E是 Hilbert C~*-模,证明了E的每个闭子模均可补的充要条件是 K(E)的每个非零遗传C~*-子代数B,均有形式B=pK(E)p,其中p为L(E)中投影元。 相似文献
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Equivalence of sketches S and T means the equivalence of their categories ModS and ModT of all Set-valued models. E. Vitale and the second author have characterized equivalence of limit-sketches by means of bimodels, where a bimodel for limit sketches S and T is a model of S in the category ModT. For general sketches, we show that an analogous result holds provided that ModT is substituted by a more complex category; e.g., in case of limit-coproduct sketches, that category is (ModT), the free product completion of ModT. 相似文献
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Satoshi Yamanaka 《代数通讯》2013,41(9):4121-4131
It seems that Morita invariance judges of the importance of classes of ring extensions concerned. Miyashita introduced the notion of Morita equivalence in ring extensions, and he showed that the classes of G-Galois extensions and Frobenius extensions are Morita invariant. After that, Ikehata showed that the classes of separable extensions, Hirata separable extensions, symmetric extensions, and QF-extensions are Morita invariant. In this article, we shall prove that the classes of several extensions are Morita invariant. Further, we will give an example of the class of ring extensions which is not Morita invariant. 相似文献
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The concept of Morita equivalence is generalized to the contextof locally C*-algebras. This generalizes a well-known theoremof Brown, Green and Rieffel, Pacific J. Math. 71 (1977) 349363.2000 Mathematics Subject Classification 46L08, 46L05. 相似文献
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On the Morita Equivalence of Tensor Algebras 总被引:4,自引:0,他引:4
We develop a notion of Morita equivalence for general C*-correspondencesover C*-algebras. We show that if two correspondences are Moritaequivalent, then the tensor algebras built from them are stronglyMorita equivalent in the sense developed by Blecher, Muhly andPaulsen. Also, the Toeplitz algebras are strongly Morita equivalentin the sense of Rieffel, as are the CuntzPimsner algebras.Conversely, if the tensor algebras are strongly Morita equivalent,and if the correspondences are aperiodic in a fashion that generalizesthe notion of aperiodicity for automorphisms of C*-algebras,then the correspondences are Morita equivalent. This generalizesa venerated theorem of Arveson on algebraic conjugacy invariantsfor ergodic, measure-preserving transformations. The notionof aperiodicity, which also generalizes the concept of fullConnes spectrum for automorphisms, is explored; its role inthe ideal theory of tensor algebras and in the theory of theirautomorphisms is investigated. 1991 Mathematics Subject Classification:46H10, 46H20, 46H99, 46M99, 47D15, 47D25. 相似文献
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Let n
i
,m
j
> 1. In [5], the sperical noncommutative torus
was defined by twisting
in
by a totally skew multiplier p on
for T
pd
a pd-homogeneous C*-algebra over
. It is shown that
is strongly Morita equivalent to
.
This work is supported by Grant No. 1999-2-102-001-3 from the interdisciplinary research program year of the KOSEF 相似文献
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Pere Ara 《Algebras and Representation Theory》1999,2(3):227-247
We develop the theory of Morita equivalence for rings with involution, and we show the corresponding fundamental representation theorem. In order to allow applications to operator algebras, we work within the class of idempotent nondegenerate rings. We also prove that two commutative rings with involution are Morita *-equivalent if and only if they are *-isomorphic. 相似文献