The Solvable Lie Algebras with Filiform R_n Nilradicals

In this paper we explicitly determine automorphism group of filiform Lie algebra Rn to find the indecomposable solvable Lie algebras with filiform Lie algebra Rn nilradicals.We also prove that the indecomposable solvable Lie algebras with filiform Rn nilradicals is complete.

India＇s Engagement With Indonesia： Potentiality Lies in Air Services

Global financial crisis and subsequent protectionist measures of US government motivated Indian government to look for opportunities towards ASEAN nations through ＂Look East Policy.＂ While scouting for opportunities, it was found that Indonesian air services market is buoyant and promising where Indonesia has recently liberalized its open sky policies for inviting domestic as well as foreign investment. Time is appropriate for Indian government to negotiate on how India can participate in Indonesian domestic market and provide air services to its consumers. The paper tries to analyze how Indian private domestic airlines can enter into the markets of Indonesia and whether they would be able to provide such services. It further tries to examine that certain value addition services in terms of auxiliary air services are currently required for Indonesia. To that extent, how is India going to capitalize such opportunities by providing such competitive value addition services？ Indonesia is currently witnessing frequent air accidents and making safety as a major concern for consumers. It tries to argue whether India can provide technical and other support services to reduce such hazards. The research methodology includes Input-Output Table calculating using WIOD （World Input Output Database） database. National Input-Output Table for analyzing Indonesian air services was also consulted for authors＇ own calculations

The Normative Value of Truth and the Problem of Lie

The article concerns the normative value of truth in relation to lie. Based on arguments derived primarily from ancient philosophers （Eubulides, Plato, Aristotle）, medieval philosophers （St. Augustine, St. Thomas Aquinas）, the thinker of the Renaissance---Machiavelli, the main philosopher of the Enlightenment--Kant, the 19th-century author of Beyond Good and Evil （Nietzsche）, and contemporary thinkers such as Derrida and Lacan, the author considers here truth as a normative value. Lying is relative to the truth, and it has no ontological legitimacy, even it cannot exist without truth itself. In the final part of the article, the author concludes that the truth, however, cannot lead to clearly had effects, be harmful or cause pain disproportionate to the effects caused by lie. Therefore, it must coexist with the good--the other parent value. Only when both values complement each other can we talk about the normative value of truth. The truth should be correlated with other values on which value systems are based, especially the good of a person or group of persons, avoiding harm towards others, and the protection of a person＇s health and life. Only then can the truth be appropriate to use. It is not an immovable foundation, but a dynamically functioning value, in which language and the ethical （active） dimensions provide the value of the specified situations. The truth can be a double-edged sword： It may hurt, but it can defend itself. The latter function seems to be the most important type of the normativity of truth.

“谎言”

太阳渐渐地落下山了，夜慢慢地沉了下来，但是蝉还在因燥热而不停地大声抱怨。 天气异常闷热，一点儿风都没有。“但愿上天正在酝酿一场突如其来的暴风雨。”我想着，锁好车，快步朝家走去，躲进空调房也许是躲避闷热的唯一办法。

Displacement manifold method for type synthesis of lower-mobility parallel mechanisms

Type synthesis of lower-mobility parallel mechanisms is a hot and frontier topic in international academic and industrial field. Based on the Lie group theory, a displacement manifold synthesis method is proposed. For all the nine kinds of lower-mobility parallel mechanisms, the mechanism displacement manifold, limb displacement manifold and the geometrical conditions which guarantee that the intersection of the limb displacement manifold is the desired mechanism displacement manifold are enumerated. Various limb kinematic chains can be obtained using the product closure of displacement subgroup. Parallel mechanisms can be constructed with these limbs while obeying the geometrical conditions. Hence, all the nine kinds of lower-mobility parallel mechanisms can be synthesized using this method. Since displacement manifold deals with finite motion, the result mechanism of synthesis have full-cycle mobility. Novel architectures of lower-mobility parallel mechanisms can be obtained using this method.

Simple algebras of Weyl type

Over a fieldF of arbitrary characteristic, we define the associative and the Lie algebras of Weyl type on the same vector spaceA[D] =A?F[D] from any pair of a commutative associative algebra,A with an identity element and the polynomial algebraF[D] of a commutative derivation subalgebraD ofA We prove thatA[D], as a Lie algebra (modulo its center) or as an associative algebra, is simple if and only ifA isD-simple andA[D] acts faithfully onA. Thus we obtain a lot of simple algebras.

On Non-Abelian Extensions of 3-Lie Algebras

In this paper, we study non-abelian extensions of 3-Lie algebras through Maurer-Cartan elements. We show that there is a one-to-one correspondence between isomorphism classes of non-abelian extensions of 3-Lie algebras and equivalence classes of Maurer-Cartan elements in a DGLA. The structure of the Leibniz algebra on the space of fundamental objects is also analyzed.

On Rigid 2-Step Nilpotent Lie Algebras

In this note we consider 2-step nilpotent Lie algebras and give a criterion for the rigidity of this class in the variety N2n of 2-step nilpotent Lie algebras of dimension n. We apply this criterion to prove that every rigid Lie algebra in N2n is indecomposable, except for η3 C and η3 η3.

Lie Triple Derivations on von Neumann Algebras

Let A be a von Neumann algebra with no central abelian projections. It is proved that if an additive map δ :A → A satisfies δ([[a, b], c]) = [[δ(a), b], c] + [[a, δ(b)], c] +[[a, b], δ(c)] for any a, b, c∈ A with ab = 0(resp. ab = P, where P is a fixed nontrivial projection in A), then there exist an additive derivation d from A into itself and an additive map f :A → ZA vanishing at every second commutator [[a, b], c] with ab = 0(resp.ab = P) such that δ(a) = d(a) + f(a) for any a∈ A.

The centralizer of an element in a Lie algebra of type L

In this paper, we investigate the Lie algebra L(A,α,δ) of type L and obtain the respective sufficient conditions for L(A,α,δ δ to be semisimple, and for Z(ω) = Fω as well, where 0 ≠ ω ? L(A, α, δ, δ) and Z(ω) is the centralizer of ω.

Double Derivations of n-Lie Superalgebras

Let g be an n-Lie superalgebra. We study the double derivation algebra 7）（g） and describe the relation between 7）（9） and the usual derivation Lie superalgebra Der（9）. We show that the set 7）（9） of all double derivations is a subalgebra of the general linear Lie superalgebra gl（9） and the inner derivation algebra ad（9） is an ideal of 7）（9）. We also show that if 9 is a perfect n-Lie superalgebra with certain constraints on the base field, then the centralizer of ad（9） in 7P（9） is trivial. Finally, we give that for every perfect n-Lie superalgebra 9, the triple derivations of the derivation algebra Der（9） are exactly the derivations of Der（9）.

A new kind of graded Lie algebra and parastatistical supersymmetry

In this paper the usual Z2 graded Lie algebra is generalized to a new form, which may be called Z2,2 graded Lie algebra. It is shown that there exist close connections between the Z2,2 graded Lie algebra and parastatistics, so the Z2,2 can be used to study and analyse various symmetries and supersymmetries of the paraparticle systems.

Geometric orbit datum and orbit covers

Vogan conjectured that the parabolic induction of orbit data is independent of the choice of the parabolic subgroup. In this paper we first give the parabolic induction of orbit covers, whose relationship with geometric orbit datum is also induced. Hence we show a geometric interpretation of orbit data and finally prove the conjugation for geometric orbit datum using geometric method.

Lie Triple Derivations of the Lie Algebra of Dominant Block Upper Triangular Matrices

Let N be the Lie algebra of all n x n dominant block upper triangular matrices over a field F. In this paper, we explicitly describe all Lie triple derivations of N when char（F） ≠ 2. As an application, we characterize Lie derivations of N when char（F） ≠ 2.

Determinant formula and a realization for the Lie algebra W(2,2)

In this paper, an explicit determinant formula is given for the Verma modules over the Lie algebra W(2, 2). We construct a natural realization of a certain vaccum module for the algebra W(2, 2) via the Weyl vertex algebra. We also describe several results including the irreducibility, characters and the descending filtrations of submodules for the Verma module over the algebra W(2, 2).