Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Projective representations of abelian groups

Authors: N. B. Backhouse and C. J. Bradley
Journal: Proc. Amer. Math. Soc. 36 (1972), 260-266
MSC: Primary 22D12
MathSciNet review: 0308329
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ \omega $ be a factor system for the locally compact abelian group G. Then we show that the finite-dimensional unitary irreducible projective representations of G, having factor system $ \omega $, possess a common dimension $ d(\omega )$. Using a characterisation of $ d(\omega )$ as the index in G of a maximal subgroup on which $ \omega $ is symmetric we derive a formula for $ d(\omega )$ in the case that G is discrete and finitely generated.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 22D12

Retrieve articles in all journals with MSC: 22D12

Additional Information

Keywords: Locally compact abelian group, projective representation, factor system, Kronecker product, abelian group, finitely generated abelian group
Article copyright: © Copyright 1972 American Mathematical Society