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D J Britten - One of the best experts on this subject based on the ideXlab platform.

  • tensor products of Torsion free c n modules of finite degree and finite dimensional modules
    Communications in Algebra, 2006
    Co-Authors: D J Britten, Justin Lariviere, Frank Lemire
    Abstract:

    It is known that every Torsion free C n -module of finite degree is completely reducible. In this article, we provide a formula for the decomposition of the tensor product of a Simple Torsion free C n -module of finite degree with a Simple finite dimensional C n -module. As a byproduct we obtain a recursion formula for the decomposition of the tensor product of any two Simple finite dimensional C n -modules.

  • Submodule Lattice of Generalized Verma Modules
    Communications in Algebra, 2003
    Co-Authors: D J Britten, Vyacheslav Futorny, F. W. Lemire
    Abstract:

    Abstract Let 𝒢 be a Simple finite dimensional Lie algebra over the complex numbers and let 𝒢¯ = 𝒢1 ⊕…⊕ 𝒢 k be a regular semiSimple subalgebra of 𝒢 with each 𝒢 i being a Simple algebra of type A or C. It is shown that the lattice of submodules of a generalized Verma 𝒢-module constructed by parabolic induction starting from a Simple Torsion free 𝒢¯-module is almost always isomorphic to the lattice of submodules of an associated module formed as a quotient of a classical Verma module by a sum of Verma submodules. In particular, it is shown that the Mathieu admissible Verma modules involved have maximal submodules which are the sum of Verma modules.

  • tensor product realizations of Simple Torsion free modules
    Canadian Journal of Mathematics, 2001
    Co-Authors: D J Britten, Frank Lemire
    Abstract:

    LetG be a finite dimensional Simple Lie algebra over the complex numbers C. Fernando reduced the classification of infinite dimensional SimpleG-modules with a finite dimensional weight space to determining the Simple Torsion freeG-modules forG of type A or C. These modules were determined by Mathieu and using his work we provide a more elementary construction realizing each one as a submodule of an easily constructed tensor product module.

  • On modules of bounded multiplicities for the symplectic algebras
    Transactions of the American Mathematical Society, 1999
    Co-Authors: D J Britten, F. W. Lemire
    Abstract:

    Simple infinite dimensional highest weight modules having bounded weight multipicities are classified as submodules of a tensor product. Also, it is shown that a Simple Torsion free module of finite degree tensored with a finite dimensional module is completely reducible.

  • A constraint on the existence of Simple Torsion free Lie modules
    Proceedings of the American Mathematical Society, 1995
    Co-Authors: D J Britten, Frank Lemire, Vahid Tarokh
    Abstract:

    For any Simple Lie algebra L with Cartan subalgebra H the classification of all Simple H-diagonalizable L-modules having a finite-dimensional weight space is known to depend on determining the Simple Torsion-free Lmodules of finite degree. It is further known that the only Simple Lie algebras which admit Simple Torsion-free modules of finite degree are those of types An and Cn . For the case of An we show that there are no Simple Torsion-free Anmodules of degree k for n > 4 and 2 1, and C,, n > 2, possess Torsion-free modules. It is easy to see that no Simple Torsion-free modules of minimal weight space dimension greater than 1 exist for A1 . The existence of Simple Torsion-free An-modules of arbitrary degree for n = 2, 3 has been established in [BBL]. In this note, we further restrict the existence of Torsion-free A,-modules by proving Main Theorem. There are no Simple Torsion-free A,-modules of degree k for n>4 and 2< k

Frank Lemire - One of the best experts on this subject based on the ideXlab platform.

  • tensor products of Torsion free c n modules of finite degree and finite dimensional modules
    Communications in Algebra, 2006
    Co-Authors: D J Britten, Justin Lariviere, Frank Lemire
    Abstract:

    It is known that every Torsion free C n -module of finite degree is completely reducible. In this article, we provide a formula for the decomposition of the tensor product of a Simple Torsion free C n -module of finite degree with a Simple finite dimensional C n -module. As a byproduct we obtain a recursion formula for the decomposition of the tensor product of any two Simple finite dimensional C n -modules.

  • tensor product realizations of Simple Torsion free modules
    Canadian Journal of Mathematics, 2001
    Co-Authors: D J Britten, Frank Lemire
    Abstract:

    LetG be a finite dimensional Simple Lie algebra over the complex numbers C. Fernando reduced the classification of infinite dimensional SimpleG-modules with a finite dimensional weight space to determining the Simple Torsion freeG-modules forG of type A or C. These modules were determined by Mathieu and using his work we provide a more elementary construction realizing each one as a submodule of an easily constructed tensor product module.

  • A constraint on the existence of Simple Torsion free Lie modules
    Proceedings of the American Mathematical Society, 1995
    Co-Authors: D J Britten, Frank Lemire, Vahid Tarokh
    Abstract:

    For any Simple Lie algebra L with Cartan subalgebra H the classification of all Simple H-diagonalizable L-modules having a finite-dimensional weight space is known to depend on determining the Simple Torsion-free Lmodules of finite degree. It is further known that the only Simple Lie algebras which admit Simple Torsion-free modules of finite degree are those of types An and Cn . For the case of An we show that there are no Simple Torsion-free Anmodules of degree k for n > 4 and 2 1, and C,, n > 2, possess Torsion-free modules. It is easy to see that no Simple Torsion-free modules of minimal weight space dimension greater than 1 exist for A1 . The existence of Simple Torsion-free An-modules of arbitrary degree for n = 2, 3 has been established in [BBL]. In this note, we further restrict the existence of Torsion-free A,-modules by proving Main Theorem. There are no Simple Torsion-free A,-modules of degree k for n>4 and 2< k

  • a constraint on the existence of Simple Torsion free lie modules
    Proceedings of the American Mathematical Society, 1995
    Co-Authors: D J Britten, Frank Lemire, Vahid Tarokh
    Abstract:

    For any Simple Lie algebra L with Cartan subalgebra H the classification of all Simple H-diagonalizable L-modules having a finite-dimensional weight space is known to depend on determining the Simple Torsion-free Lmodules of finite degree. It is further known that the only Simple Lie algebras which admit Simple Torsion-free modules of finite degree are those of types An and Cn . For the case of An we show that there are no Simple Torsion-free Anmodules of degree k for n > 4 and 2 1, and C,, n > 2, possess Torsion-free modules. It is easy to see that no Simple Torsion-free modules of minimal weight space dimension greater than 1 exist for A1 . The existence of Simple Torsion-free An-modules of arbitrary degree for n = 2, 3 has been established in [BBL]. In this note, we further restrict the existence of Torsion-free A,-modules by proving Main Theorem. There are no Simple Torsion-free A,-modules of degree k for n>4 and 2< k

Ch. Tsakmakis - One of the best experts on this subject based on the ideXlab platform.

  • Discussion of Finite Deformation Viscoelasticity Laws with Reference to Torsion Loading
    Continuum Mechanics and Thermodynamics, 2000
    Co-Authors: Norbert Huber, Ch. Tsakmakis
    Abstract:

    In a previous paper two classes of finite deformation viscoelasticity laws, referred to as Model A and Model B, respectively, have been introduced. They were derived as finite deformation counterparts of two well-known spring-dashpot linear solids, the first one being a spring in parallel with a Maxwell element and the second model consisting of a spring in series with a Kelvin element. In particular, two special forms of the free energy function related to Model A (respectively to Model B) were considered, implying two different finite deformation viscoelasticity laws referred to as Model A1 and Model A2 (respectively Model B1 and Model B2). In the present paper we discuss predicted responses of these models with reference to Simple Torsion as well as Torsion with free ends. Generally, the investigations of the paper have fundamental character in what concerns the basic concepts in formulating viscoelastic models of rate type.

  • Finite deformation plasticity and viscoplasticity laws exhibiting nonlinear hardening rules
    Computational Mechanics, 2000
    Co-Authors: E. Diegele, St. Hartmann, Ch. Tsakmakis
    Abstract:

      We consider two finite deformation plasticity models, which differ mainly in the evolution equation governing the response of kinematic hardening. Both models reduce to the same constitutive law in the case of small deformations. The aim of the paper is to discuss these models by calculating the predicted responses for some representative loading conditions. The numerical calculations needed are performed by using an efficient time-integration algorithm which has been developed with a view to implementation in the ABAQUS finite element code. Generally, there are some differences between the predicted responses and in particular between the second-order effects predicted by the two models. For some Simple deformation processes, e.g. Simple shear and Simple Torsion, the differences concerning second-order effects exhibit some kind of regularities, which are independent of material parameters. Also, even if boundary value problems are considered where global deformations are small, significant differences can exist between the predicted model responses according to the finite deformation and the limiting small deformation theory.

Najib A. Kasti - One of the best experts on this subject based on the ideXlab platform.

  • Zigzag Carbon Nanotubes under Simple Torsion – Structural Mechanics Formulation
    Advanced Materials Research, 2012
    Co-Authors: Najib A. Kasti
    Abstract:

    When using structural mechanics to study the deformation of carbon nanotubes (CNTs), one has to pick the structural mechanics properties that are equivalent to the molecular mechanics properties. In a previous publication [1], we have determined the relation between the bending stiffness EI/a used in structural mechanics and the bond bending stiffness C used in molecular mechanics for zigzag carbon nanotubes under Simple tension. This paper extends the concept and determines the corresponding relation for Simple Torsion. We show that the relation obtained is different than that of Simple tension; in Simple Torsion, EI/a is load and chirality dependent. However, for the particular case of a graphene sheet, Simple tension and Torsion lead to the same value of EI/a, namely C/2. We also include the structural mechanics deformation of the tube that accounts for axial, bending and Torsional structural stiffnesses. Unlike Simple tension, the deformation in the case of Simple Torsion has the axial stiffness coupled to the bending and Torsional stiffnesses.

  • zigzag carbon nanotubes under Simple Torsion structural mechanics formulation
    Advanced Materials Research, 2012
    Co-Authors: Najib A. Kasti
    Abstract:

    When using structural mechanics to study the deformation of carbon nanotubes (CNTs), one has to pick the structural mechanics properties that are equivalent to the molecular mechanics properties. In a previous publication [1], we have determined the relation between the bending stiffness EI/a used in structural mechanics and the bond bending stiffness C used in molecular mechanics for zigzag carbon nanotubes under Simple tension. This paper extends the concept and determines the corresponding relation for Simple Torsion. We show that the relation obtained is different than that of Simple tension; in Simple Torsion, EI/a is load and chirality dependent. However, for the particular case of a graphene sheet, Simple tension and Torsion lead to the same value of EI/a, namely C/2. We also include the structural mechanics deformation of the tube that accounts for axial, bending and Torsional structural stiffnesses. Unlike Simple tension, the deformation in the case of Simple Torsion has the axial stiffness coupled to the bending and Torsional stiffnesses.

Vahid Tarokh - One of the best experts on this subject based on the ideXlab platform.

  • A constraint on the existence of Simple Torsion free Lie modules
    Proceedings of the American Mathematical Society, 1995
    Co-Authors: D J Britten, Frank Lemire, Vahid Tarokh
    Abstract:

    For any Simple Lie algebra L with Cartan subalgebra H the classification of all Simple H-diagonalizable L-modules having a finite-dimensional weight space is known to depend on determining the Simple Torsion-free Lmodules of finite degree. It is further known that the only Simple Lie algebras which admit Simple Torsion-free modules of finite degree are those of types An and Cn . For the case of An we show that there are no Simple Torsion-free Anmodules of degree k for n > 4 and 2 1, and C,, n > 2, possess Torsion-free modules. It is easy to see that no Simple Torsion-free modules of minimal weight space dimension greater than 1 exist for A1 . The existence of Simple Torsion-free An-modules of arbitrary degree for n = 2, 3 has been established in [BBL]. In this note, we further restrict the existence of Torsion-free A,-modules by proving Main Theorem. There are no Simple Torsion-free A,-modules of degree k for n>4 and 2< k

  • a constraint on the existence of Simple Torsion free lie modules
    Proceedings of the American Mathematical Society, 1995
    Co-Authors: D J Britten, Frank Lemire, Vahid Tarokh
    Abstract:

    For any Simple Lie algebra L with Cartan subalgebra H the classification of all Simple H-diagonalizable L-modules having a finite-dimensional weight space is known to depend on determining the Simple Torsion-free Lmodules of finite degree. It is further known that the only Simple Lie algebras which admit Simple Torsion-free modules of finite degree are those of types An and Cn . For the case of An we show that there are no Simple Torsion-free Anmodules of degree k for n > 4 and 2 1, and C,, n > 2, possess Torsion-free modules. It is easy to see that no Simple Torsion-free modules of minimal weight space dimension greater than 1 exist for A1 . The existence of Simple Torsion-free An-modules of arbitrary degree for n = 2, 3 has been established in [BBL]. In this note, we further restrict the existence of Torsion-free A,-modules by proving Main Theorem. There are no Simple Torsion-free A,-modules of degree k for n>4 and 2< k