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941.
In this paper a class of two-parameter weak Hopf algebras wrτ,s(g) corresponding to Borcherds-Cartan matrix is constructed. This class consists of noncommutative and noncocommutative weak Hopf algebras but not Hopf algebras. It can be viewed as a generalized class of one-parameter weak Hopf algebras wUq(g). 相似文献
942.
943.
In this paper we proceed into the next step of formalization of a consistent dual theory for mass dimension one spinors. This task is developed approaching the two different and complementary aspects of such duals, clarifying its algebraic structure and the so called τ-deformation. The former regards the mathematical equivalence of the recent proposed Lorentz preserving dual with the duals of algebraic spinors, from Clifford algebras, showing the consistency and generality of the new dual. Moreover, by revealing its automorphism structure, the hole of the τ-deformation and contrasting the action group orbits with other Lorentz breaking scenarios, we argue that the new mass dimension one dual theory is placed over solid and consistent basis. 相似文献
944.
An approach for q-deformed Bogoliubov transformations is presented. Assuming a left-right module action together with an ?-operation and deformed commutation relations, we construct a q-deformation of the nonlinear Bogoliubov transformation. Finally, we introduce a Hopf structure when q is a root of unity. 相似文献
945.
利用欧几里德若当代数技术,在单调的条件下,用内积的方法证明了对称锥互补问题的一类FB互补函数相应的势函数的水平集有界性. 该方法在理论和应用上相较于以往用迹不等式证明势函数水平集有界性更具普适性和推广价值. 在设计算法求解势函数的无约束极小化问题时,水平集有界性是保证下降算法收敛的重要条件,因此,对算法的设计具有理论意义. 相似文献
946.
George W. Bluman Omar Mrani-Zentar Deshin Finlay 《Journal of Nonlinear Mathematical Physics》2018,25(4):528-557
It is shown explicitly how one can obtain elements of Lie groups as compositions of products of other elements based on the commutator properties of associated Lie algebras. Problems of this kind can arise naturally in control theory. Suppose an apparatus has mechanisms for moving in a limited number of ways with other movements generated by compositions of allowed motions. Two concrete examples are: (1) the restricted parallel parking problem where the commutator of translations in y and rotations in the xy-plane yields translations in x. Here the control problem involves a vehicle that can only perform a series of translations in y and rotations with the aim of efficiently obtaining a pure translation in x; (2) involves an apparatus that can only perform rotations about two axes with the aim of performing rotations about a third axis. Both examples involve three-dimensional Lie algebras. In particular, the composition problem is solved for the nine three- and four-dimensional Lie algebras with non-trivial solutions. Three different solution methods are presented. Two of these methods depend on operator and matrix representations of a Lie algebra. The other method is a differential equation method that depends solely on the commutator properties of a Lie algebra. Remarkably, for these distinguished Lie algebras the solutions involve arbitrary functions and can be expressed in terms of elementary functions. 相似文献
947.
给出半单Nelson代数的一些新性质,证明了全序半单Nelson代数只存在二阶和三阶的,四阶及以上的有限全序半单Nelson代数不存在.同时,借助数学软件Mathematica得到阶数不超过9的全部(同构意义下)半单Nelson代数. 相似文献
948.
In this paper, we study (n-1)-order deformations of an n-Lie algebra and introduce the notion of a Nijenhuis operator on an n-Lie algebra, which could give rise to trivial deformations. We prove that a polynomial of a Nijenhuis operator is still a Nijenhuis operator. Finally, we give various constructions of Nijenhuis operators and some examples. 相似文献
949.
Gerd Niestegge 《Foundations of Physics》2008,38(3):241-256
The well-known proposal to consider the Lüders-von Neumann measurement as a non-classical extension of probability conditionalization
is further developed. The major results include some new concepts like the different grades of compatibility, the objective
conditional probabilities which are independent of the underlying state and stem from a certain purely algebraic relation
between the events, and an axiomatic approach to quantum mechanics. The main axioms are certain postulates concerning the
conditional probabilities and own intrinsic probabilistic interpretations from the very beginning. A Jordan product is derived
for the observables, and the consideration of composite systems leads to operator algebras on the Hilbert space over the complex
numbers, which is the standard model of quantum mechanics. The paper gives an expository overview of the results presented
in a series of recent papers by the author. For the first time, the complete approach is presented as a whole in a single
paper. Moreover, since the mathematical proofs are already available in the original papers, the present paper can dispense
with the mathematical details and maximum generality, thus addressing a wider audience of physicists, philosophers or quantum
computer scientists. 相似文献
950.
Andrzej Łuczak 《International Journal of Theoretical Physics》2008,47(1):236-244
We investigate a quantum counterpart of the classical notion of a stochastic process continuous with probability one, and
prove that the L
2-limit of quantum martingales ‘continuous with probability one’ is a quantum martingale ‘continuous with probability one’.
Applications of this result to a number of concrete situations is presented. 相似文献