A class of simple Lie groups whose quasirepresentations with small defect can be approximated by an ordinary representation
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We prove that every connected Lie group with finite center (as is well known, the semisimple groups of this kind admit no nontrivial real pseudocharacters) satisfies the following triviality theorem (which thus is not a characterization of amenable groups of this kind): every locally bounded finite-dimensional quasirepresentation of such a group with sufficiently small defect admits a close ordinary representation of the group.
Abstract
We prove that every connected Lie group with finite center (as is well known, the semisimple groups of this kind admit no nontrivial real pseudocharacters) satisfies the following triviality theorem (which thus is not a characterization of amenable groups of this kind): every locally bounded finite-dimensional quasirepresentation of such a group with sufficiently small defect admits a close ordinary representation of the group.
참고문헌 (2)
- A. I. Shtern, "Quasisymmetry. I", Russ. J. Math. Phys., 2(3), pp.353~382 (1994)
- A. I. Shtern, "Finite-dimensional quasirepresentations of connected Lie groups and Mishchenko’s conjecture", Fundam. Prikl. Mat., 13(7), pp.85~225 (2007)