Chapter

Unitary groups

Adam M. Bincer

in Lie Groups and Lie Algebras

Published in print October 2012 | ISBN: 9780199662920
Published online January 2013 | e-ISBN: 9780191745492 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199662920.003.0013
Unitary groups

More Like This

Show all results sharing this subject:

  • Mathematical and Statistical Physics

GO

Show Summary Details

Preview

Unitary groups are defined. An explicit choice of generators in the defining representation is displayed and used to abstract commutation relations for u(n). It is shown that the center of U(n) has the structure of Zn. It follows that for n 〉 2 complex representations exist and that complex conjugation is an outer automorphism. It is shown that independent Casimirs can be constructed as polynomials in the generators of degree k, where 1 ≤ kn for U(n) while k = 1 should be omitted for SU(n). It is noted that for n 〉 2 a cubic Casimir is present in the integrity basis for SU(n), which in general gives rise to anomalies.

Keywords: unitary groups; unitary algebras; generators; center; automorphisms; Casimirs; anomaly

Chapter.  2197 words. 

Subjects: Mathematical and Statistical Physics

Full text: subscription required

How to subscribe Recommend to my Librarian

Buy this work at Oxford University Press »

Users without a subscription are not able to see the full content. Please, subscribe or login to access all content.