A note on the multipliers and and projective representations of semi-simple Lie groups

Bagchi, Bhaskar ; Misra, Gadadhar (2000) A note on the multipliers and and projective representations of semi-simple Lie groups Sankhya - Series A, 62 (A3). pp. 425-432. ISSN 0581-572X

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Abstract

We show that, for any connected semi-simple Lie group G, there is a natural isomorphism between the Galois cohomology H2(G, T) (with respect to the trivial action of G on the circle group T) and the Pontryagin dual of the homology group H1(G) (with integer coefficients) of G as a manifold. As an application, we find that there is a natural correspondence between the projective representations of any such group and a class of ordinary representations of its universal cover. We illustrate these ideas with the example of the group of bi-holomorphic automorphisms of the unit disc.

Item Type:Article
Source:Copyright of this article belongs to Indian Statistical Institute.
Keywords:Semi-simple Lie Groups; Projective Repesentatives; Multipliers
ID Code:66997
Deposited On:28 Oct 2011 10:30
Last Modified:18 May 2016 14:18

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