Crossed product algebras: representation, Brauer group and application.

56 p.

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Bibliographic Details
Main Author:	Feng, Yongqi
Other Authors:	Frédérique Oggier
Format:	Theses and Dissertations
Published:	2014
Subjects:	DRNTU::Science::Mathematics::Algebra
Online Access:	http://hdl.handle.net/10356/57394
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Institution:	Nanyang Technological University

id	sg-ntu-dr.10356-57394
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spelling	sg-ntu-dr.10356-573942023-02-28T23:36:06Z Crossed product algebras: representation, Brauer group and application. Feng, Yongqi Frédérique Oggier School of Physical and Mathematical Sciences DRNTU::Science::Mathematics::Algebra 56 p. In this master thesis we study a special kind of central simple algebras called crossed product algebras. We will show how to construct them and study some of their properties, mainly their representation theory and divisibility. In particular, Brauer groups are employed to study the divisibility of crossed product algebras. A special kind of crossed product algebra called cyclic algebra has relatively simple structure and is particularly interesting. We compute the representation and Brauer group, of cyclic algebras and construct a new cyclic algebra with higher degree by tensoring two cyclic algebras with lower degree. Motivated by a coding theory problem, we next discuss the existence of unitary involution over crossed product algebras. We will show that the Hermitian conjugation of the representation matrix can be translated into the assumption of this involution. These generalize the results in [51. Finally we discuss how to find unitary elements in crossed product algebras. Master of Science 2014-04-07T10:21:48Z 2014-04-07T10:21:48Z 2011 2011 Thesis http://hdl.handle.net/10356/57394 Nanyang Technological University application/pdf
institution	Nanyang Technological University
building	NTU Library
continent	Asia
country	Singapore Singapore
content_provider	NTU Library
collection	DR-NTU
topic	DRNTU::Science::Mathematics::Algebra
spellingShingle	DRNTU::Science::Mathematics::Algebra Feng, Yongqi Crossed product algebras: representation, Brauer group and application.
description	56 p.
author2	Frédérique Oggier
author_facet	Frédérique Oggier Feng, Yongqi
format	Theses and Dissertations
author	Feng, Yongqi
author_sort	Feng, Yongqi
title	Crossed product algebras: representation, Brauer group and application.
title_short	Crossed product algebras: representation, Brauer group and application.
title_full	Crossed product algebras: representation, Brauer group and application.
title_fullStr	Crossed product algebras: representation, Brauer group and application.
title_full_unstemmed	Crossed product algebras: representation, Brauer group and application.
title_sort	crossed product algebras: representation, brauer group and application.
publishDate	2014
url	http://hdl.handle.net/10356/57394
_version_	1759853904645849088

Crossed product algebras: representation, Brauer group and application.

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