Orientador: Prof. Dr. Roldão da Rocha jr. / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Matemática , 2014. / Clifford algebras in Hilbert spaces are studied, along with the possible defnitions
of spinors when the classical Clifford algebra is equipped with an additional structure of
algebra C. The groups associated with the Clifford algebras, such as the Clifford-Lipschtz
groups, Pin and Spin groups, are introduced together with unitary structures and trace
operators in Clifford algebras in Hilbert spaces as well. Von-Neumann algebras are studied
and the Bogoliubov automorphism is used to generalize the twisted Clifford-Lipschtz
groups, using the graduation in Clifford algebra with the additional structure of algebra
C. Fock representations and Hilbert-Schmidt operators are going to be introduced in the
exterior algebra underlying the Clifford algebras in Hilbert spaces. In addition, twisted
Clifford-Lipschitz groups can be constructed with the Bogoliubov automorphism, when it
is an inner automorphism. This defines the Pin and Spin groups in the Clifford algebra
with the additional structure of algebra C.
| Identifer | oai:union.ndltd.org:IBICT/oai:BDTD:77354 |
| Date | January 2014 |
| Creators | Lima, Rian Lopes de |
| Contributors | Rocha Junior, Roldão da, Machado, Daniel Miranda, Struchiner, Ivan, Kuznetsova, Zhanna G. |
| Source Sets | IBICT Brazilian ETDs |
| Language | Portuguese |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, info:eu-repo/semantics/masterThesis |
| Format | application/pdf, 144 f. : il. |
| Source | reponame:Repositório Institucional da UFABC, instname:Universidade Federal do ABC, instacron:UFABC |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | http://biblioteca.ufabc.edu.br/index.php?codigo_sophia=77354&midiaext=70818, http://biblioteca.ufabc.edu.br/index.php?codigo_sophia=77354&midiaext=70817, Cover: http://biblioteca.ufabc.edu.brphp/capa.php?obra=77354 |
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