Groups with faithful irreducible projective unitary representations
Copyright policy )Groups with faithful irreducible projective unitary representations
For a countable group G and a multiplier c on G with values in the circle, we study the property of G having a unitary projective c-representation which is both irreducible and projectively faithful. We show that this property is equivalent to G being the quotient of an appropriate group by its centre. A criterion is given in terms of the minisocle of G. Several examples are described to show the existence of various behaviours.
27 pages
- University of Rennes 1 France
- Université de Rennes 1 France
- University of Rennes 2 France
- University of Geneva Switzerland
- Mathematics Research Institute of Rennes France
capable groups, groups with FAb property, irreducible projective unitary representation, [MATH.MATH-RT]Mathematics [math]/Representation Theory [math.RT], Projective unitary representations, Stem covers, Capable groups, Unitary representations of locally compact groups, Group Theory (math.GR), faithful irreducible representations, 20C25, 22D10, Projectively faithful representations, Central extensions, FOS: Mathematics, 20C25, [MATH.MATH-RT] Mathematics [math]/Representation Theory [math.RT], 22D10, Projective representations and multipliers, Mathematics - Group Theory, Irreducible representations
capable groups, groups with FAb property, irreducible projective unitary representation, [MATH.MATH-RT]Mathematics [math]/Representation Theory [math.RT], Projective unitary representations, Stem covers, Capable groups, Unitary representations of locally compact groups, Group Theory (math.GR), faithful irreducible representations, 20C25, 22D10, Projectively faithful representations, Central extensions, FOS: Mathematics, 20C25, [MATH.MATH-RT] Mathematics [math]/Representation Theory [math.RT], 22D10, Projective representations and multipliers, Mathematics - Group Theory, Irreducible representations
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