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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
51

Existence of algebras of symmetry-classes of tensors with respect to translation-in-variant pairs

Hillel, Joel S. January 1968 (has links)
The notion of the 'classical' multilinear maps such as the symmetric and skew-symmetric maps, has the following generalization: given a vector-space V and a pair (H[subscript n],X[subscript n]) where is a subgroup of the symmetric group S[subscript n] and X[subscript n] is a character of H[subscript n], we consider multilinear maps from V[superscript n] (n-fold cartesian product of V ) into any other vector space, which are ‘symmetric with respect to (H[subscript n],X[subscript n])’, i.e., which have a certain symmetry in their values on permuted tuples of vectors, where the permutations are in H[subscript n]. Given a pair (H[subscript n],X[subscript n]) and a vector-space V , we can construct a space V[superscript (n)] over V through which the maps 'symmetric with respect to (H[subscript n],X[subscript n])’ linearize. The space V[superscript (n)] is usually defined abstractly by means of a certain universal mapping property and gives the tensor, symmetric and Grassmarm spaces for the 'classical' maps. Given a sequence of pairs [formula omitted]and the corresponding spaces V[superscript (n)], we let [formula omitted] (where V[superscript b]) is the ground field). In the classical cases, A has a natural multiplicative operation which makes A an algebra, i.e., the Tensor, Symmetric and Grassmann algebras. This presentation has been motivated by the attempt to generalize the construction of an algebra A to a wider family of 'admissible' sequences of pairs [formula omitted]. This consideration has led us to investigate permutation groups on the numbers 1,2,3,… which are closed under a certain 'shift' of the permutations, i.e., if [formula omitted] is a permutation, we define [formula omitted] and we call a permutation group H 'translation-invariant' if for every [formula omitted] is also in H . We begin our presentation by characterising the 'translation-invariant' groups. We show that the study of these (infinite) groups can be reduced to the study of certain finite groups. Then, we proceed to discuss the lattice of the translation-invariant groups. Finally, we show that a translation-invariant group H , together, with an appropriate character X of H , represents an equivalence class of 'admissible' sequences of pairs [formula omitted]. For a particular choice of representatives of the equivalence class, we can construct an algebra of 'symmetry classes of tensors' which generalizes the Tensor, Symmetric and Grassmann algebras. / Science, Faculty of / Mathematics, Department of / Graduate
52

Algebras arising in theoretical genetics

Kwei, John T.P. January 1971 (has links)
Certain non-associative algebras have important applications in theoretical Mendelian Genetics. In this thesis we will give definitions to these algebras and study their properties. Some examples will also be given. / Science, Faculty of / Mathematics, Department of / Graduate
53

Sobre a semissimplicidade de álgebras de Hopf finito-dimensionais e o duplo de Drinfeld

Martini, Grasiela January 2013 (has links)
Neste trabalho discutimos a semissimplicidade de álgebras de Hopf finito-dimensionais e construímos o Duplo de Drinfeld D(H) de uma tal álgebra H. Além disso, apresentamos um resultado mostrando a equivalência entre as categorias de representações dos módulos sobre D(H) e dos módulos de Yetter-Drinfeld sobre Hcop. Como consequência deste estudo, apresentamos um resultado que caracteriza uma álgebra de Hopf quase triangular. / In this work we discuss the semisimplicity of some finite-dimensional Hopf Algebras and we set up the Drinfel’d double D(H) of such an algebra H. In addiction, we present a result showing the equivalence between the representation category of modules over D(H) and the Yetter-Drinfeld modules over Hcop. As a consequence of this, we present a result that features a quasitriangular Hopf algebra.
54

On the product of linear forms /

Mertens, Robert Lee January 1973 (has links)
No description available.
55

Foundations of the Hopf invariant in topology

Lee, Kon-Ying January 1970 (has links)
No description available.
56

Measure algebras and their Stone spaces

Chan, Donald January 1977 (has links)
No description available.
57

Q-algebras and related topics

Yamaguchi, Ryuji January 1976 (has links)
No description available.
58

3-dimensional symplectic geometries and metasymplectic geometries

Chung, K-W. January 1989 (has links)
No description available.
59

A*-algebras and Minimal Ideals in Topological Rings

Wei, Jui-Hung 05 1900 (has links)
The present thesis mainly concerns B*-algebras, A*-algebras, and minimal ideals in topological rings.
60

Deformed Poisson W-algebras of type A

Walker, Lachlan Duncan January 2018 (has links)
For the algebraic group SLl+1(C) we describe a system of positive roots associated to conjugacy classes in its Weyl group Sl+1. Using this we explicitly describe the algebra of regular functions on certain transverse slices to conjugacy classes in SLl+1(C) as a polynomial algebra of invariants. These may be viewed as an algebraic group analogue of certain parabolic invariants that generate the W-algebra in type A found by Brundan and Kleshchev.

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