R. Campoamor-Stursberg

Obtainment of internal labelling operators as broken Casimir operators by means of contractions related to reduction chains in semisimple Lie algebra

Luis J. Boya†

Commutativity of missing label operators in term

A new matrix method for the Casimir operators of the Lie algebras wsp(N

Abstract. A method is given to determine the Casimir operators of the perfect Lie algebras wsp (N,R) =sp (2N,R) − → ⊕ Γω1 ⊕Γ0hN and the inhomogeneous Lie algebras Isp (2N,R) in terms of polynomials associated to a parametrized (2N +1)×(2N +1)matrix. For the inhomogeneous symplectic algebras this matrix is shown to be associated to a faithful representation. The method is extended to other classes of Lie algebras, and some applications to the missing label problem are given. PACS numbers: 02.20S2 1

Non-solvable contractions of semisimple Lie algebras in low dimension

Abstract. The problem of non-solvable contractions of Lie algebras is analyzed. By means of a stability theorem, the problem is shown to be deeply related to the embeddings among semisimple Lie algebras and the resulting branching rules for representations. With this procedure, we determine all deformations of indecomposable Lie algebras having a nontrivial Levi decomposition onto semisimple Lie algebras of dimension n ≤ 8, and obtain the non-solvable contractions of the latter class of algebras. PACS numbers: 02.20Sv, 02.20Qs2 1

Quasi-classical Lie algebras and their contractions

Abstract. After classifying indecomposable quasi-classical Lie algebras in low dimension, and showing the existence of non-reductive stable quasi-classical Lie algebras, we focus on the problem of obtaining sufficient conditions for a quasi-classical Lie algebras to be the contraction of another quasi-classical algebra. It is illustrated how this allows to recover the Yang-Mills equations of a contraction by a limiting process, and how the contractions of an algebra may generate a parameterized families of Lagrangians for pairwise non-isomorphic Lie algebras. PACS numbers: 02.20Sv, 02.20Qs, 11.15Kc2 1

Internal labelling operators and contractions of Lie algebras

Abstract. We analyze under which conditions the missing label problem associated to a reduction chain s ′ ⊂ s of (simple) Lie algebras can be completely solved by means of an Inönü-Wigner contraction g naturally related to the embedding. This provides a new interpretation of the missing label operators in terms of the Casimir operators of the contracted algebra, and shows that the available labeling operators are not completely equivalent. Further, the procedure is used to obtain upper bounds for the number of invariants of affine Lie algebras arising as contractions of semisimple algebras. PACS numbers: 02.20Sv, 02.20Qs2 1

Non-solvable contractions of simple Lie algebras in low dimension‡

Abstract. The problem of non-solvable contractions of Lie algebras is analyzed. By means of a stability theorem, the problem is shown to be deeply related to the embeddings among semisimple Lie algebras and the resulting branching rules for representations. With this procedure, we determine all deformations of indecomposable Lie algebras having a nontrivial Levi decomposition onto semisimple Lie algebras of dimension n ≤ 8, and obtain the non-solvable contractions of the latter class of algebras

MANUFACTURE METHODS COMPARISON AND CHARACTERIZATION OF CONDUCTIVE GLASS REINFORCED PLASTICS BY ADDING CARBON NANOFIBRES

Nowadays, the use of composite materials is widely extended for many applications, especially in aeronautics and transportation. Glass Reinforced Plastics (GRPs) are one of those materials which are commonly used due to their properties and strength. In order to give electrical conductivity to this kind of composites, this work proposes the us