The intersection of kernels of the finite-dimensional pure pseudorepresentations of connected semisimple Lie groups
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As is well known, every finite-dimensional representation andevery finite-dimensional pseudorepresentation of a connected semisimple Liegroup is continuous, and the kernel of every finite-dimensional pseudorepresentationof a connected Lie group is a closed normal subgroup of theLie group. There are two natural questions, namely, what are the connectedsemisimple Lie groups for which the intersection of kernels of thefinite-dimensional pure pseudorepresentations reduced to the identity element(“the connected semisimple Lie groups that are finite-dimensionallypseudorepresentable”), and how to describe the intersection of kernels of thefinite-dimensional pure pseudorepresentations of a general connected semisimpleLie group.
Abstract
As is well known, every finite-dimensional representation andevery finite-dimensional pseudorepresentation of a connected semisimple Liegroup is continuous, and the kernel of every finite-dimensional pseudorepresentationof a connected Lie group is a closed normal subgroup of theLie group. There are two natural questions, namely, what are the connectedsemisimple Lie groups for which the intersection of kernels of thefinite-dimensional pure pseudorepresentations reduced to the identity element(“the connected semisimple Lie groups that are finite-dimensionallypseudorepresentable”), and how to describe the intersection of kernels of thefinite-dimensional pure pseudorepresentations of a general connected semisimpleLie group.
참고문헌 (6)
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