CLASSIFICATION OF (n + 2)-DIMENSIONAL METRIC n-LIE ALGEBRAS

In this paper, we give the classification of (n + 2)-dimensional metric n-Lie algebras in terms of some facts about n-Lie algebras.     

DERIVATIONS OF THE 3-LIE ALGEBRA REALIZED BY gl(n, ℂ)

This paper studies structures of the 3-Lie algebra M realized by the general linear Lie algebra gl(n, ?). We show that M has only one nonzero proper ideal. We then give explicit expressions of both derivations and inner derivations of M. Finally, we investigate substructures of the (inner) derivation algebra of M.     

Remarks on l-conformal extension of the Newton-Hooke algebra

The l-conformal extension of the Newton-Hooke algebra proposed in [J. Negro, M.A. del Olmo, A. Rodriguez-Marco, J. Math. Phys. 38 (1997) 3810] is formulated in the basis in which the flat space limit is unambiguous. Admissible central charges are specified. The infinite-dimensional Virasoro-Kac-Moody type extension is given.     

P-Twisted Affine Lie Algebras and Their Associated Vertex Algebras

For any finite-dimensional semisimple Lie algebra g, a Z＋-graded vertex algebra is construsted on the vacuum representation Vk（g[θ]of g[θ]）,which is a one-dimentionM central extension of 8-invariant subspace on the loop algebra Lg=g C（（t^1/p））.     

多项式角动量代数的代数表示及实现

本文利用三参数李群求代数表示的方法求出多项式角动量代数的代数表示及其酉表示，找到一个能同时承载李代数及相对应的多项式角动量代数的基底，并在该基底下求出两种代数之间的联系，利用该联系则也可求出多项式角动量代数的代数表示.最后求出多项式角动量代数的单玻色实现及其在有限维多项式函数空间的微分实现. 关键词： 多项式角动量代数 Higgs代数 su(2)代数     

Simple Axioms for Orthomodular Implication Algebras

Simple, independent axioms for orthomodular implication algebras are presented.     

THE ADJOINT REPRESENTATION OF QUANTUM ALGEBRA Uq(sl(2))

Starting from any representation of the Lie algebra on the finite dimensional vector space V we can construct the representation on the space Aut(V). These representations are of the type of ad. That is one of the reasons, why it is important to study the adjoint representation of the Lie algebra on the universal enveloping algebra U(). A similar situation is for the quantum groups U_q(). In this paper, we study the adjoint representation for the simplest quantum algebra U_q(sl(2)) in the case that q is not a root of unity.     

On the q-Deformation of Heisenberg Algebra

This paper deals with a class of q-deformations of Heisenberg algebra which contains the q-Heisenberg algebra, the q-oscillator algebra and others. Their representation theory is considered for q being generic or a root of 1. Finally, the structure of Hopf algebra in a quotient algebra is also discussed.     

A mathematical structure for the generalization of conventional algebra

An abstract mathematical framework is presented in this paper as a unification of several deformed or generalized algebra proposed recently in the context of generalized statistical theories intended to treat certain complex thermodynamic or statistical systems. It is shown that, from a mathematical point of view, any bijective function can in principle be used to formulate an algebra in which the conventional algebraic rules are generalized.      

Applications of Polynomial Algebras to 2-Dimensional Deformed Oscillators

The polynomial algebra is a deformed su（2） algebra. Here, we use polynomial algebra az a method to solve a series of deformed oscillators. Thus, we find a series of physics systems corresponding with polynomial algebra with different highest orders.     

Free field realization of the level-2 elliptic algebra Ux,p ([^(\mathfraks\mathfrakl)]2 )*)U_{x,p} (\widehat{\mathfrak{s}\mathfrak{l}}_2 )*)

We give a level-2 representation of the elliptic algebra in terms of one free boson and one free fermion. We show that -modules have a natural direct sum decomposition into the irreducible (deformed) super-Virasoro modules associated with the coset . Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005.     

P-Twisted Affine Lie Algebras and Their Associated Vertex Algebras

For any finite-dimensional semisimple Lie algebra g, a Z₊-graded vertex algebra is construsted on the vacuum representation V_k(\hat{g}[ θ]) of \hat{g}[θ], which is a one-dimentional central extension of θ-invariant subspace on the loop algebra Lg=g\otimes C((t^1/p)).     

Entropy of Partitions on Sequential Effect Algebras

By using the sequential effect algebra theory, we establish the partitions and refinements of quantum logics and study their entropies.     

Differential geometry of the Lie algebra of the quantum plane

We present a differential calculus on the extension of the quantum plane obtained by considering that the (bosonic) generator x is invertible and by working with polynomials in ln x instead of polynomials in x. We construct the quantum Lie algebra associated with this extension and obtain its Hopf algebra structure and its dual Hopf algebra.     

A Unified Algebraic Approach to Quantum Theory

Conventional approaches to quantum mechanics are essentially dualistic. This is reflected in the fact that their mathematical formulation is based on two distinct mathematical structures: the algebra of dynamical variables (observables) and the vector space of state vectors. In contrast, coherent interpretations of quantum mechanics highlight the fact that quantum phenomena must be considered as undivided wholes. Here, we discuss a purely algebraic formulation of quantum mechanics. This formulation does not require the specification of a space of state vectors; rather, the required vector spaces can be identified as substructures in the algebra of dynamical variables (suitably extended for bosonic systems). This formulation of quantum mechanics captures the undivided wholeness characteristic of quantum phenomena, and provides insight into their characteristic nonseparability and nonlocality. The interpretation of the algebraic formulation in terms of quantum process is discussed.     

Nonstandard Poincaré and Heisenberg Algebras

Nonstandard deformations of the Poincaré group Fun(P(1+1)) and its dual enveloping algebra U (p(1+1)) are obtained as a contraction of the h-deformed (Jordanian) quantum group Fun( SL _h (2)) and its dual. A nonstandard quantization of the Heisenberg algebra U(h(1)) is also investigated.     

Multiboson Realizations of Lie and Quant urn Algebras

A unified method to construct the (multi-)boson realizations of the Lie and quantum algebras is proposed based on a universal deformation of boson (Heisenberg-Weyl) algebra and its multiboson realization. Some explicit examples, the Lie algebras sl(2) and su (Ill), q-boson algebra, quantum algebras sl(2)_q and su (l,l)_q, along with the q-ladder algebra are studied in detail. In particular, the square boson realizations of su (1,l) and su (l,l)_q are naturally obtained as special cases.     

Applications of Polynomial Algebras to 2-Dimensional Deformed Oscillators

The polynomial algebra is a deformed su(2) algebra. Here, we use polynomial algebra as a method to solve a series of deformed oscillators. Thus, we find a series of physics systems corresponding with polynomial algebra with different highest orders.     

W∞ Algebra and High-Order Virasoro Algebra

We give the relation between W_∞ algebra and high-order Virasoro algebra (HOVA), i.e., W_∞ algebra is the limit of HOVA. Then we give the super high-order Virasoro algebra from super W_∞ algebra.