UID:
almahu_9948233584302882
Umfang:
1 online resource (x, 227 pages) :
,
digital, PDF file(s).
Ausgabe:
Second edition.
ISBN:
9780511565755 (ebook)
Inhalt:
To an algebraist the theory of group characters presents one of those fascinating situations, where the structure of an abstract system is elucidated by a unique set of numbers inherent in the system. But the subject also has a practical aspect, since group characters have gained importance in several branches of science, in which considerations of symmetry play a decisive part. This is an introductory text, suitable for final-year undergraduates or postgraduate students. The only prerequisites are a standard knowledge of linear algebra and a modest acquaintance with group theory. Especial care has been taken to explain how group characters are computed. The character tables of most of the familiar accessible groups are either constructed in the text or included amongst the exercise, all of which are supplied with solutions. The chapter on permutation groups contains a detailed account of the characters of the symmetric group based on the generating function of Frobenius and on the Schur functions. The exposition has been made self-sufficient by the inclusion of auxiliary material on skew-symmetric polynomials, determinants and symmetric functions.
Anmerkung:
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
,
Group representations -- Elementary properties of group characters -- Induced characters -- Permutation groups -- Group-theoretical applications -- Arithmetic properties of group characters -- Real representations -- Appendix: A generalisation of Vandermonde's determinant -- The alternant quotient -- Jacobi's theorem on inverse matrices -- Quadratic forms -- Congruence relations in an algebraic number field.
Weitere Ausg.:
Print version: ISBN 9780521332460
Sprache:
Englisch
URL:
https://doi.org/10.1017/CBO9780511565755
