Research Doctorate - Doctor of Philosophy (PhD) / (**Note: this abstract is a plain text version of the author's abstract, the original of which contains characters and symbols which cannot be accurately represented in this format. The properly formatted abstract can be viewed in the Abstract and Thesis files above.**) Let (G,G+) be a quasi-lattice-ordered group with positive cone G+ Laca and Raeburn have shown that the universal C*-algebra C*(G,G+)introduced by Nica is a crossed product BG+ Xɑ G+ by a semigroup of endomorphisms. Subsequent research centered on totally ordered abelian groups. We generalize the results in [2], [3] and [5] to extend it to the case of discrete lattice-ordered abelian groups. In particular given a hereditary subsemigroup H+ of G+ we introduce a closed ideal IH+ of the C*-algebra BG+. We construct an approximate identity for this ideal and show that IH+ is extendibly a-invariant. It follows that there is an isomorphism between C*-crossed products (BG+/IH+) XɑG+ and B(G/H)+ XβG+. This leads to one of our main results that B(G/H)+ XβG+ is realized as an induced C*-algebra IndG-H (B(G/H+ Xt(G/H)+). Then we use this result to show the existence of the following short exact sequence of C*-algebras 0-IH+ XɑG+ → BG+ XɑG+ → IndG-H (B(G/H+ Xt(G/H)+) → 0. This leads to show that the ideal IH+ XɑG+ is generated by {iBG+(1-1u):u∊H+} and therefore contained in the commutator ideal CG of the C*-algebra BG+ XɑG+. Moreover, we use our short exact sequence to study the primitive ideals of the C* algebra BG+ XɑG+ which is isomorphic to the Toeplitz albebra T(G) of G.

Research Doctorate - Doctor of Philosophy (PhD) / (**Note: this abstract is a plain text version of the author's abstract, the original of which contains characters and symbols which cannot be accurately represented in this format. The properly formatted abstract can be viewed in the Abstract and Thesis files above.**) Let (G,G+) be a quasi-lattice-ordered group with positive cone G+ Laca and Raeburn have shown that the universal C*-algebra C*(G,G+)introduced by Nica is a crossed product BG+ Xɑ G+ by a semigroup of endomorphisms. Subsequent research centered on totally ordered abelian groups. We generalize the results in [2], [3] and [5] to extend it to the case of discrete lattice-ordered abelian groups. In particular given a hereditary subsemigroup H+ of G+ we introduce a closed ideal IH+ of the C*-algebra BG+. We construct an approximate identity for this ideal and show that IH+ is extendibly a-invariant. It follows that there is an isomorphism between C*-crossed products (BG+/IH+) XɑG+ and B(G/H)+ XβG+. This leads to one of our main results that B(G/H)+ XβG+ is realized as an induced C*-algebra IndG-H (B(G/H+ Xt(G/H)+). Then we use this result to show the existence of the following short exact sequence of C*-algebras 0-IH+ XɑG+ → BG+ XɑG+ → IndG-H (B(G/H+ Xt(G/H)+) → 0. This leads to show that the ideal IH+ XɑG+ is generated by {iBG+(1-1u):u∊H+} and therefore contained in the commutator ideal CG of the C*-algebra BG+ XɑG+. Moreover, we use our short exact sequence to study the primitive ideals of the C* algebra BG+ XɑG+ which is isomorphic to the Toeplitz albebra T(G) of G.

Made available in DSpace on 2014-06-11T19:26:55Z (GMT). No. of bitstreams: 0 Previous issue date: 2008-04-18Bitstream added on 2014-06-13T20:08:05Z : No. of bitstreams: 1 galao_ph_me_sjrp.pdf: 533527 bytes, checksum: e6eea706db9ff1f10f8ba9df3a1fdea7 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Este trabalho tem como objetivo principal o cálculo do grupo de homotopia de alguns grupos clássicos, como o grupo das rotações do espaço Euclidiano Rn, SO(n), o grupo unitário U(n), seu subgrupo especial unitário SU(n) e o grupo simpléetico Sp(n). Para esses cálculos usaremos seqüências exatas e propriedades relacionadas à fibrados. / The main purpose of this work is to calculate homotopy groups of some classical groups as the rotation groups of the euclidean space Rn, SO(n), the unitary group U(n), your special unitary subgroup SU(n) and the symplectic group Sp(n). For these calculus we will use exact sequences and properties relacionated to the fibre bundle. Keywords: Exact Sequences, Fibre Bundle, Classical Groups, Homotopy Groups.

Submitted by TAÍSA FERNANDA DE LIMA QUEMEL null (taisafernanda.10@hotmail.com) on 2016-03-10T20:25:22Z No. of bitstreams: 1 Versão final_Dissertação_Taísa Quemel.pdf: 674351 bytes, checksum: 3498053a8bb53e50ac3119a10d45a0c5 (MD5) / Approved for entry into archive by Ana Paula Grisoto (grisotoana@reitoria.unesp.br) on 2016-03-11T12:17:58Z (GMT) No. of bitstreams: 1 quemel_tfl_me_sjrp.pdf: 674351 bytes, checksum: 3498053a8bb53e50ac3119a10d45a0c5 (MD5) / Made available in DSpace on 2016-03-11T12:17:58Z (GMT). No. of bitstreams: 1 quemel_tfl_me_sjrp.pdf: 674351 bytes, checksum: 3498053a8bb53e50ac3119a10d45a0c5 (MD5) Previous issue date: 2016-02-26 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / O objetivo deste trabalho é mostrar que πn(X) é sempre abeliano quando n ≥ 2 e que π1(X) é abeliano quando X for um H-espaço e por fim calcular alguns grupos de homotopia utilizando sequência exata de uma fibração. / The goal of this work is to show that πn(X) is always abelian when n ≥ 2 and that π1(X) is abelian when X is an H-space and finally calculate some homotopy groups using the exact sequence of a fibration.

Orientador: João Peres Vieira / Banca: Ermínia de Lourdes Campello Fanti / Banca: Denise de Mattos / Resumo: Este trabalho tem como objetivo principal o cálculo do grupo de homotopia de alguns grupos clássicos, como o grupo das rotações do espaço Euclidiano Rn, SO(n), o grupo unitário U(n), seu subgrupo especial unitário SU(n) e o grupo simpléetico Sp(n). Para esses cálculos usaremos seqüências exatas e propriedades relacionadas à fibrados. / Abstract:The main purpose of this work is to calculate homotopy groups of some classical groups as the rotation groups of the euclidean space Rn, SO(n), the unitary group U(n), your special unitary subgroup SU(n) and the symplectic group Sp(n). For these calculus we will use exact sequences and properties relacionated to the fibre bundle. Keywords: Exact Sequences, Fibre Bundle, Classical Groups, Homotopy Groups. / Mestre