LOCAL AUTOMORPHISMS OF SEMISIMPLE ALGEBRAS AND GROUP ALGEBRAS

Let F be a field of characteristic not 2, and let A be a finite-dimensional semisimple F -algebra. All local automorphisms of A are characterized when all the degrees of A are larger than 1. If F is further assumed to be an algebraically closed field of characteristic zero, K a finite group, F K the group algebra of K over F , then all local automorphisms of F K are also characterized.

Co-splitting of Simple Lie Algebras of Type A, D, E

In this paper, through a meticulous description of finite root system,a concrete comultiplication with an explicit action on the basis elements of finitedimensional simple Lie algebras of type A; D; E is constructed. Then any finitedimensional simple Lie algebra of type A; D; E is endowed with a new generalizedLie coalgebra splitting. This construction verifies the known existence of a co-splitLie structure on any finite dimensional complex simple Lie algebra.

Non-linear Maps on Borel Subalgebras of Simple Lie Algebras Preserving Abelin Ideals

Let g be a complex simple Lie algebra of rank ι, b the standard Borel subalgebra. An invertible map on Ь is said to preserve abelian ideals if it maps each abelian ideal to some such ideal of the same dimension. In this article, by using some results of Chevalley groups, the theory of root systems and root space decomposition, the author gives an explicit description on such maps of Ь.

Linear Commuting Maps on Parabolic Subalgebras of Finite-dimensional Simple Lie Algebras

A map φ on a Lie algebra g is called to be commuting if [φ(x), x] = 0 for all x ∈ g. Let L be a finite-dimensional simple Lie algebra over an algebraically closed field F of characteristic 0, P a parabolic subalgebra of L. In this paper, we prove that a linear mapφon P is commuting if and only if φ is a scalar multiplication map on P.

A Class of Simple Modules for Electrical Lie Algebra of Type D_(5)

The simple modules for electrical Lie algebra of type D5 were investigated.The sufficient and necessary criteria of the simple Z-graded highest weight modules were established by means of determining the singular vectors of the Verma modules.The simple highest weight module is isomorphic to either that for the symplectic Lie algebra sp4 or Verma module.

Hopf Algebra of Labeled Simple Graphs

A lot of combinatorial objects have a natural bialgebra structure. In this paper, we prove that the vector space spanned by labeled simple graphs is a bialgebra with the conjunction product and the unshuffle coproduct. In fact, it is a Hopf algebra since it is graded connected. The main conclusions are that the vector space spanned by labeled simple graphs arising from the unshuffle coproduct is a Hopf algebra and that there is a Hopf homomorphism from permutations to label simple graphs.

求解N-S方程SIMPLE算法的半交错网格研究

运用半交错网格设置对不可压缩流动的 Navier- Stokes方程进行数值离散求解 ,文中对不合理压力场产生的原因及抑制方法进行了探讨 ,导出了压力控制体界面上速度的修正表达式。作为算例 ,本文采用区域湍流模化方法 ,在核心区采用标准 k-ε模型 ,在近壁区采用单方程低雷诺数模型 ,对封闭转 -静盘腔、具有径向出流的转 -静盘腔和非规则环形通道内的流动进行了数值模拟 ,并与实验数据进行了对比分析 。

A Simple Jerky Dynamics,Genesio System

The third order explicit autonomous differential equations named as jerk equations represent an interesting subclass of dynamical systems that can exhibit many major features of the regular and chaotic motion. In this paper, we show that an algebraically simple system, the Genesio system can be recast into a jerky dynamics and its jerk equation can be derived from one-dimensional Newtonian equation. We also investigate the global dynamical properties of the corresponding jerk system.

Derivations of the Schrodinger Algebra on Restricted Simple Modules

Over an algebraically closed field of characteristic p>2,based on the results on the representation theory of special linear Lie algebra sl(2),restricted simple modules L(λ) of the Schrodinger algebra S(1)are determined,and all derivations of S(1)on L(λ)are also obtained.As an application,the first cohomology of S(1)with the coefficient in L(λ)is determined.

A Characterization of The Twisted Heisenberg-Virasoro Vertex Operator Algebra

The twisted Heisenberg-Virasoro algebra is the universal central extension of the Lie algebra of differential operators on a circle of order at most one.In this paper,we first study the variety of semi-conformal vectors of the twisted Heisenberg-Virasoro vertex operator algebra,which is a finite set consisting of two nontrivial elements.Based on this property,we also show that the twisted Heisenberg-Virasoro vertex operator algebra is a tensor product of two vertex operator algebras.Moreover,associating to properties of semi-conformal vectors of the twisted Heisenberg-Virasoro vertex operator algebra,we charaterized twisted Heisenberg-Virasoro vertex operator algebras.This will be used to understand the classification problems of vertex operator algebras whose varieties of semi-conformal vectors are finite sets.

Control of seismic and operational vibrations of rotating machines using semi-active mounts

A dual isolation problem for rotating machines consists of isolation of housing structures from the machine vibrations and protection of machines during an earthquake to maintain their functionality. Desirable characteristics of machine mounts for the above two purposes can differ significantly due to difference in nature of the excitation and performance criteria in the two situations. In this paper, relevant response quantities are identified that may be used to quantify performance and simplified models of rotating machines are presented using which these relevant response quantities may be calculated. Using random vibration approach with a stationary excitation, it is shown that significant improvement in seismic performance is achievable by proper mount design. Results of shaking table experiments performed with a realistic setup using a centrifugal pump are presented. It is concluded that a solution to this dual isolation problem lies in a semi-active mount capable switching its properties from ‘operation-optimum’ to ‘seismic-optimum’ at the onset of a seismic event.

The Direct Sum Decomposition of Type G_2 Lie Algebra

This article mainly discusses the direct sum decomposition of type G_2 Lie algebra, which, under such decomposition, is decomposed into a type A_1 simple Lie algebra and one of its modules. Four theorems are given to describe this module,which could be the direct sum of two or three irreducible modules, or the direct sum of weight modules and trivial modules, or the highest weight module.

Multiplicity-Free Gradings on Semisimple Lie and Jordan Algebras and Skew Root Systems

A G-grading on an algebra, where G is an abelian group, is called multiplicityfree if each homogeneous component of the grading is 1-dimensional. We introduce skew root sys tems of Lie type and skew root systems of Jordan type, and use them to cons true t multiplicity-free gradings on semisimple Lie algebras and on semisimple Jordan algebras respectively. Under certain conditions the corresponding Lie (resp., Jordan) algebras are simple. Two families of skew root systems of Lie type (resp., of Jordan type) are constructed and the corresponding Lie (resp., Jordan) algebras are identified. This is a new approach to study abelian group gradings on Lie and Jordan algebras.

Fuzzy Logic and Zadeh Algebra

In this work we create a connection between AFS (Axiomatic Fuzzy Sets) fuzzy logic systems and Zadeh algebra. Beginning with simple concepts we construct fuzzy logic concepts. Simple concepts can be interpreted semantically. The membership functions of fuzzy concepts form chains which satisfy Zadeh algebra axioms. These chains are based on important relationship condition (1) represented in the introduction where the binary relation Rm of a simple concept m is defined more general in Definition 2.10. Then every chain of membership functions forms a Zadeh algebra. It demands a lot of preliminaries before we obtain this desired result.

Algebraic or Algorithmic: Searching for Optimal Solutions in Multi-Stage Supply Chain Models

In this paper we proposed an AMH Supply Chain model to obtain optimal solutions for Two-, Three- and Four-Stage for deterministic models. Besides deriving its algebraic solutions, a simple searching method is successfully applied in obtaining optimal total costs and its integer multipliers. Our model has shown promising results in comparison to Equal Cycle Time and other existing ones. The tests focused on obtaining optimal total annual costs and other related details of Two-, Three- and Four-Stage for deterministic models. The results are run under Visual Basic Programming platform using Intel? CoreTM2 Duo T6500 Processor.

Semi-Simple Algebras and Normality of Closed Subsets in Standard Table Algebras

By using Artin-Wedderburn Theorem and the decomp- osition of central edepotent, several results about normality on closed subsets in standard table algebras are generalized to complex semi-simple algebras and the proofs are easier than the original ones.

The Realization of 4-dimensional 3-Lie Algebras

In this paper, we mainly investigate the realization of 3-Lie algebras from a family of Lie algebras. We prove the realization theorem, offer a concrete example realizing all type of 4-dimensional 3-Lie algebras, and also give some properties about semi-simple n-Lie algebras.

Minimal systems of generators for central division algebra and semi-simple algebra

Suppose that F is a field of characteristic zero and (ⅰ) D is a finite-dimensional central division algabra over F; (ⅱ) A is a finite-dimensional semi-simple algabra over F. It is proved that as F-algebras, D and A can be generated by two elements respectively.

量子Loop代数U_(q)(L(sl_(2)))的单权模

用构造的方法解决量子Loop代数U_(q)(L(sl_(2)))具有一个一维权空间的单权模的结构问题,得到了任意一个具有一维权空间的单权模必同构于U_(q)(L(sl_(2)))的四类单权模之一.此外,还构造了一类权空间维数为2的既非最高权也非最低权的量子Loop代数U_(q)(L(sl_(2)))的单权模.

有限维单李代数的伴随表示分解

利用有限维单李代数根空间分解,给出复数域上有限维单李代数的根链;利用复数域上不可约sl(2,C)-模的分类,给出有限维单李代数g在伴随作用下分解成g的不可约sl(2,C)-子模直和的分解式.