Geometric Algebra
Mostrando 13-24 de 25 artigos, teses e dissertações.
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13. Sobre a existencia de bases SAGBI finitas para o nucleo de k-derivações em k[x1,...,xn] / About the existence of finite SAGBI bases for the kernel of a k-derivation in k[x1,...,xn]
The general objective of this work is to understand the SAGBI bases theory from a structural point of view, seeking criterias for its existence and results that prove its effitiency in the study of certain subalgebras of k[x], as well as to study the general theory of derivations over polynomial rings, its localizations and quotients, in order to explo
Publicado em: 2008
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14. InformaÃÃo quÃntica e emaranhamento: uma abordagem usando Ãlgebra geomÃtrica
We studied the quantum entanglement as a quantum computation and quantum information tool. This research focused on the bipartite entanglement found between two qubits of a Heisenberg hamiltonian. The choice of this hamiltonian was motivated by the fact that it can be simulated by many distinct physical systems. Besides, the control of its parameters during
Publicado em: 2007
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15. Arithmetic fuchsian groups identified in quaternion orders for the construction of signal constellations / Grupos fuchsianos aritmeticos identificados em ordens dos quaternios para construção de constelações de sinais
Within the context of digital communications system in homogeneous space in particular, in hyperbolic spaces, it is necessary to establish systematic procedure for the construction of lattices O ; as the basic entity for construction of eometrically uniforms signal constellations. By this procedure we identify the algebraic and geometric structures to constr
Publicado em: 2007
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16. Geometric invariant theory and representations of quivers / Teoria geometrica dos invariantes e representações de quivers
This thesis is divided into two parts. ln the first part we present the main ideas and tools of Geometric lnvariant Theory, which is concerned with the following problem: ls it possible to give an algebraic structure to the quotient of an algebraic variety by the action of an algebraic group? Qne of the most important results says that an algebraic quotient
Publicado em: 2006
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17. O conceito de independência e dependência linear e os registros de representação semiótica nos livros didáticos de Álgebra Linear
This research aims to investigate which semiotic representation registers are most used in Linear Algebra textbooks in the presentation and study of the topic linear independence. The mathematics textbook is a resource much used by the teachers in its work. They present many representation registers, which can to be analyzed qualitatively to assess their pot
Publicado em: 2006
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18. UMA CONSTRUÇÃO ALGÉBRICA DE CÓDIGOS GEOMÉTRICOS / AN ALGEBRAIC CONSTRUCTION OF GEOMETRIC CODES
Começamos estudando uma classe particular de códigos lineares, os chamados códigos de Goppa que s~ao obtidos calculando o valor de certas funções em pontos de Kn, onde K é um corpo finito. Apresentamos uma generalização desta construção e definimos códigos de avaliação sobre K-álgebras satisfazendo certas propriedades. Para estes códigos, desc
Publicado em: 2005
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19. Uma seqüência de ensino para a construção de uma tabela trigonométrica
O objetivo deste estudo é construir uma tabela trigonométrica, com base em levantamentos históricos dos trabalhos de Ptolomeu e outros matemáticos da Grécia Antiga, para investigar a apropriação do significado dos conceitos das razões trigonométricas: seno, cosseno e tangente, no triângulo retângulo, por estudantes do 1o ano do Ensino Médio. Proc
Publicado em: 2005
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20. Dos complexos aos numeros de Cayley : uma abordagem geometrica
The extension ofthe numeric field beyond the complexes to the so called hypercomplex numbers is presented here through an approach which integrates the algebraic and geometric aspects of the constructions. The main goal of this dissertation was to produce an accessible text combining this two views and also aspects of the historical development of this subje
Publicado em: 2002
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21. Dimension independence in exterior algebra.
The identities between homogeneous expressions in rank 1 vectors and rank n - 1 covectors in a Grassmann-Cayley algebra of rank n, in which one set occurs multilinearly, are shown to represent a set of dimension-independent identities. The theorem yields an infinite set of nontrivial geometric identities from a given identity.
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22. A geometric identity for Pappus' theorem.
An expression in the exterior algebra of a Peano space yielding Pappus' theorem was originally given by Doubilet, Rota, and Stein [Doubilet, P., Rota, G.-C. & Stein, J. (1974) Stud. Appl. Math. 8, 185-216]. Motivated by an identity of Rota, I give an identity in a Grassmann-Cayley algebra of step 3, involving joins and meets alone, which expresses the theore
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23. Infinite flag varieties and conjugacy theorems
We study the orbit of a highest-weight vector in an integrable highest-weight module of the group G associated to a Kac-Moody algebra [unk](A). We obtain applications to the geometric structure of the associated flag varieties and to the algebraic structure of [unk](A). In particular, we prove conjugacy theorems for Cartan and Borel subalgebras of [unk](A),
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24. Semi-infinite cohomology and string theory
We develop the theory of semi-infinite cohomology of graded Lie algebras first introduced by Feigin. We show that the relative semi-infinite cohomology has a structure analogous to that of the de Rham cohomology in Kähler geometry. We prove a vanishing theorem for a special class of modules, and we apply our results to the case of the Virasoro algebra and t