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81.
Mariusz Rabus Saharon Shelah 《Proceedings of the American Mathematical Society》1999,127(9):2573-2581
For every uncountable cardinal there is a ccc Boolean algebra whose topological density is .
82.
Let T be a monad over a category A. Then a homotopy structure for A, defined by a cocylinder P : A A, or path-endofunctor, can be lifted to the category A
T
of Eilenberg–Moore algebras over T, provided that P is consistent with T in a natural sense, i.e. equipped with a natural transformation : T P P T satisfying some obvious axioms. In this way, homotopy can be lifted from well-known, basic situations to various categories of algebras for instance, from topological spaces to topological semigroups, or spaces over a fixed space (fibrewise homotopy), or actions of a fixed topological group (equivariant homotopy); from categories to strict monoidal categories; from chain complexes to associative chain algebras. The interest is given by the possibility of lifting the homotopy operations (as faces, degeneracy, connections, reversion, interchange, vertical composition, etc.) and their axioms from A to A
T
, just by verifying the consistency between these operations and : T P P T. When this holds, the structure we obtain on our category of algebras is sufficiently powerful to ensure the main general properties of homotopy. 相似文献
83.
Sergei Yu. Vasilovsky 《Proceedings of the American Mathematical Society》1999,127(12):3517-3524
The algebra of all matrices over a field has a natural -grading . In this paper graded identities of the -graded algebra over a field of characteristic zero are studied. It is shown that all the -graded polynomial identities of follow from the following:
84.
Constantin Năstăsescu Florin Panaite Freddy Van Oystaeyen 《Algebras and Representation Theory》1999,2(3):211-226
We apply to Hopf algebras a construction from graded rings, called the group ring of a graded ring. By using this construction we study the transfer of properties between certain categories of relative Hopf modules. As another application, we obtain a Maschke-type theorem for a Galois extension over a semisimple Hopf algebra. 相似文献
85.
Lars Kadison 《Algebras and Representation Theory》1999,2(4):397-414
This paper begins with an introduction to -Frobenius structure on a finite-dimensional Hopf subalgebra pair. In Section 2 a study is made of a generalization of Frobenius bimodules and -Frobenius extensions. Also a special type of twisted Frobenius bimodule which gives an endomorphism ring theorem and converse is studied. Section 3 brings together material on separable bimodules, the dual definitions of split and separable extension, and a theorem of Sugano on endomorphism rings of separable bimodules. In Section 4, separable twisted Frobenius bimodules are characterized in terms of data that generalizes a Frobenius homomorphism and a dual base. In the style of duality, two corollaries characterizing split -Frobenius and separable -Frobenius extensions are proven. Sugano"s theorem is extended to -Frobenius extensions and their endomorphism rings. In Section 5, the problem of when separable extensions are Frobenius extensions is discussed. A Hopf algebra example and a matrix example are given of finite rank free separable -Frobenius extensions which are not Frobenius in the ordinary sense. 相似文献
86.
Li Huishi 《数学年刊B辑(英文版)》1994,15(4):463-468
It is proved that for a left Noetherian z-graded ring A,if every finitely generated graded A-module has finite projective dimension(i.e-,A is gr-regular)then every finitely generated A-module has finite projective dimension(i.e.,A is regular).Some applications of this result to filtered rings and some classical cases are also given. 相似文献
87.
在弱波导近似下,计及了折射率梯度的影响,把▽ε看作微扰项,应用微扰理论,给出了修正到任一级近似的标量场方程,建立了一级修正解的一般表达式,并给出了相关参量的确定方法。最后,以抛物线折射率剖面单模光纤为例,给出了简要分析结果。 相似文献
88.
89.
Frederick?M.?KronzEmail author Tracy?A.?Lupher 《International Journal of Theoretical Physics》2005,44(8):1239-1258
It has been maintained that the physical content of a model of a system is completely contained in the C∗-algebra of quasi-local observables
that is associated with the system. The reason given for this is that the unitarily inequivalent representations of
are physically equivalent. But, this view is dubious for at least two reasons. First, it is not clear why the physical content
does not extend to the elements of the von Neumann algebras that are generated by representations of
. It is shown here that although the unitarily inequivalent representations of
are physically equivalent, the extended representations are not. Second, this view detracts from special global features
of physical systems such as temperature and chemical potential by effectively relegating them to the status of fixed parameters.
It is desirable to characterize such observables theoretically as elements of the algebra that is associated with a system
rather than as parameters, and thereby give a uniform treatment to all observables. This can be accomplished by going to larger
algebras. One such algebra is the universal enveloping von Neumann algebra, which is generated by the universal representation
of
; another is the direct integral of factor representations that are associated with the set of values of the global features.
Placing interpretive significance on the von Neumann algebras mentioned earlier sheds light on the significance of unitarily
inequivalent representations of
, and it serves to show the limitations of the notion of physical equivalence. 相似文献
90.
Recent development brings new results on the interplay of states on operator algebras and axiomatics of quantum mechanics.
Neither hidden space in the sense of Kochen and Specker nor approximate hidden variables exist on von Neumann algebras. Tracial
properties of states are connected with dispersions. The axioms on composite systems simplify to state extension properties. 相似文献