共查询到20条相似文献,搜索用时 46 毫秒
1.
Edward P. Osipov 《Letters in Mathematical Physics》1989,18(1):35-42
We introduce a class of infinite-dimensional Kac-Moody-Malcev algebras. These algebras are the generalization of Lie algebras of the Kac-Moody type to Malcev algebras. We demonstrate that the central extensions of the Kac-Moody-Malcev algebras are given by the same cocycles as in the case of Lie algebras. Analogues of Kac-Moody-Malcev algebras may be also introduced in the case of an arbitrary Riemann surface. 相似文献
2.
Run-Qiang Jian 《Letters in Mathematical Physics》2013,103(8):851-863
In this letter, we use quantum quasi-shuffle algebras to construct Rota–Baxter algebras, as well as tridendriform algebras. We also propose the notion of braided Rota–Baxter algebras, the relevant object of Rota–Baxter algebras in a braided tensor category. Examples of such new algebras are provided using quantum multi-brace algebras in a category of Yetter–Drinfeld modules. 相似文献
3.
In this article, we introduce a new class of graded algebras called quasi-Lie algebras of Witt type. These algebras can be seen as a generalization of other Witt-type algebras like Lie algebras of Witt type and their colored version, Lie color algebras of Witt type. 相似文献
4.
Anti-BZ-Structure in Effect Algebras 总被引:1,自引:0,他引:1
The definitions of sharply approximating effect algebras, anti-BZ-effect algebras, central approximating effect algebras, and S-anti-BZ-effect algebras are given, the relationships between sharply approximating effect algebras and anti-BZ-effect algebras, between central approximating effect algebras and anti-BZ-effect algebras are established, and the set of anti-BZ-sharp elements in S-anti-BZ-effect algebras is proved to be an orthomodular lattice. 相似文献
5.
Yongjian Xie Yongming Li Jiansheng Guo Fang Ren Dechao Li 《International Journal of Theoretical Physics》2011,50(4):1186-1197
As noncommutative generalizations of effect algebras, we introduce weak commutative pseudoeffect algebras. In this paper,
we prove that the generalized pseudoeffect algebras can be unitized if and only if they are weak commutative. Then we discuss
the relationships between weak commutative pseudoeffect algebras and weak commutative generalized pseudoeffect algebras. We
prove that the category of weak commutative pseudoeffect algebras is a reflective subcategory of weak commutative generalized
pseudoeffect algebras. Similarly, we introduce weak commutative pseudodifference posets and show the relationships between
weak commutative pseudoeffect algebras and weak commutative pseudodifference posets. 相似文献
6.
《Journal of Geometry and Physics》1995,16(2):149-167
We discuss the differential algebras used in Connes' approach to Yang-Mills theories with spontaneous symmetry breaking. These differential algebras generated by algebras of the form functions ⊗ matrix are shown to be skew tensor products of differential algebras with a specific matrix algebra. For that we derive a general formula for differential algebras based on tensor products of algebras. The result is used to characterize differential algebras which appear in models with one symmetry breaking scale. 相似文献
7.
We present an axiomatic formulation of a new class of infinitedimensional Lie algebras-the generalizations ofZ-graded Lie algebras with, generally speaking, an infinite-dimensional Cartan subalgebra and a contiguous set of roots. We call such algebras continuum Lie algebras. The simple Lie algebras of constant growth are encapsulated in our formulation. We pay particular attention to the case when the local algebra is parametrized by a commutative algebra while the Cartan operator (the generalization of the Cartan matrix) is a linear operator. Special examples of these algebras are the Kac-Moody algebras, algebras of Poisson brackets, algebras of vector fields on a manifold, current algebras, and algebras with differential or integro-differential cartan operator. The nonlinear dynamical systems associated with the continuum contragredient Lie algebras are also considered. 相似文献
8.
Noncommutative associative algebras are constructed which have the structure of module algebras over tensor products of pairs of quantized universal enveloping algebras. These module algebras decompose into multiplicity free direct sums of irreducible modules, yielding quantum analogues of generalized Howe dualities. 相似文献
9.
MICHEL DUBOIS-VIOLETTE 《Pramana》2012,78(6):947-961
We discuss the notion of Poincaré duality for graded algebras and its connections with the Koszul duality for quadratic Koszul algebras. The relevance of the Poincaré duality is pointed out for the existence of twisted potentials associated to Koszul algebras as well as for the extraction of a good generalization of Lie algebras among the quadratic-linear algebras. 相似文献
10.
Stefan Weinzierl 《Frontiers of Physics》2016,11(3):111206
In this paper I discuss Hopf algebras and Dyson–Schwinger equations. This paper starts with an introduction to Hopf algebras, followed by a review of the contribution and application of Hopf algebras to particle physics. The final part of the paper is devoted to the relation between Hopf algebras and Dyson–Schwinger equations. 相似文献
11.
《Physics letters. [Part B]》1988,214(3):371-373
We give a construction of the Virasoro algebra in terms of bilinear combinations of currents. The currents satisfy the Kac-Moody-Malcev commutation relations. The Kac-Moody-Malcev algebras are the generalization of Lie algebras of Kac-Moody type to the Malcev algebras. Thus, we give the generalization of the Sugawara construction to the case of Kac-Moody-Malcev algebras. 相似文献
12.
Basic algebras are a generalization of MV-algebras, also including orthomodular lattices and lattice effect algebras. A pre-ideal
of a basic algebra is a non-empty subset that is closed under the addition ⊕ and downwards closed with respect to the underlying
order. In this paper, we study the pre-ideal lattices of algebras in a particular subclass of basic algebras which are closer
to MV-algebras than basic algebras in general. We also prove that finite members of this subclass are exactly finite MV-algebras. 相似文献
13.
In this paper, by introducing an entropy of Markov evolution algebras, we treat the isomorphism of S-evolution algebras. A family of Markov evolution algebras is defined through the Hadamard product of structural matrices of non-negative real S-evolution algebras, and their isomorphism is studied by means of their entropy. Furthermore, the isomorphism of S-evolution algebras is treated using the concept of relative entropy. 相似文献
14.
J.M. Escobar J. Núñez P. Pérez-Fernández 《Journal of Nonlinear Mathematical Physics》2018,25(3):358-374
In this paper, we deal with contractions of Lie algebras. We use two invariant functions of Lie algebras as a tool, named ψ and ? function, respectively, which have a great application in Physics due to their remarkable properties. We focus the study of these functions in the frame of the filiform Lie algebras, trying to extend to these algebras some of the properties of such functions over semi-simple Lie algebras. 相似文献
15.
Anatolij Dvurečenskij 《Foundations of Physics》2013,43(11):1314-1338
We define a new class of pseudo effect algebras, called kite pseudo effect algebras, which is connected with partially ordered groups not necessarily with strong unit. In such a case, starting even with an Abelian po-group, we can obtain a noncommutative pseudo effect algebra. We show how such kite pseudo effect algebras are tied with different types of the Riesz Decomposition Properties. Kites are so-called perfect pseudo effect algebras, and we define conditions when kite pseudo effect algebras have the least non-trivial normal ideal. 相似文献
16.
In two earlier articles we constructed algebraic-geometric families of genus one (i.e. elliptic) Lie algebras of Krichever–Novikov
type. The considered algebras are vector fields, current and affine Lie algebras. These families deform the Witt algebra,
the Virasoro algebra, the classical current, and the affine Kac–Moody Lie algebras respectively. The constructed families
are not equivalent (not even locally) to the trivial families, despite the fact that the classical algebras are formally rigid.
This effect is due to the fact that the algebras are infinite dimensional. In this article the results are reviewed and developed
further. The constructions are induced by the geometric process of degenerating the elliptic curves to singular cubics. The
algebras are of relevance in the global operator approach to the Wess–Zumino–Witten–Novikov models appearing in the quantization
of Conformal Field Theory. 相似文献
17.
ZHANG Yu-Feng DONG Huang-He Honwah Tam 《理论物理通讯》2007,48(2):215-226
Starting from the subgroups of the group U(n), the corresponding Lie algebras of the Lie algebra Al are presented, from which two well-known simple equivalent matrix Lie algebras are given. It follows that a few expanding Lie algebras are obtained by enlarging matrices. Some of them can be devoted to producing double integrable couplings of the soliton hierarchies of nonlinear evolution equations. Others can be used to generate integrable couplings involving more potential functions. The above Lie algebras are classified into two types. Only one type can generate the integrable couplings, whose Hamiltonian structure could be obtained by use of the quadratic-form identity. In addition, one condition on searching for integrable couplings is improved such that more useful Lie algebras are enlightened to engender. Then two explicit examples are shown to illustrate the applications of the Lie algebras. Finally, with the help of closed cycling operation relations, another way of producing higher-dimensional Lie algebras is given. 相似文献
18.
Lawrence J. Landau 《Letters in Mathematical Physics》1992,25(1):47-50
The Cirel'son bound for the EPR experimental set-up provides a test of the distributivity of the observable algebra and is thus satisfied by Jordan algebras and distributive Segal algebras. By means of nondistributive algebras, the Cirel'son bound may be violated and the Rastall limit attained. It is also shown that Sherman's nondistributive Segal algebras are unsuitable as algebraic models of physical systems. 相似文献
19.
本文总结了计算黑克、布劳、及伯曼 温采尔代数在各种工数链下诱导及分导系数的线性方程方法(LEM)。特别强调了关于A,B,C,D型李代数及其量子情形与其中心代数之间的舒尔 魏尔 布劳双关性关系。这一关系使我们能够利用相应中心代数的诱导及分导系数计算出经典李代数及其量子情形的耦合与重新耦合系数。讨论了从该方法得到B,C,D型李代数不可约表示克罗内克积分解的应用。基于LEM还得到了处理对应于置换群CG系列问题的黑克代数张量积的方法。 相似文献
20.
Sylvia Pulmannová 《International Journal of Theoretical Physics》2004,43(7-8):1573-1585
Divisible effect algebras and their relations to convex effect algebras and MV-algebras are studied. A categorical equivalence between divisible effect algebras and rational vector spaces is proved. Infinitesimal, sharp and extremal elements in divisible effect algebras are studied and their relations to properties of the state space are shown. 相似文献