Title: The structure of locally bounded finite-dimensional representations of connected locally compact groups

An analogue of a Lie theorem is obtained for (not necessarily continuous) finite-dimensional representations of soluble finite-dimensional locally compact groups with connected quotient group by the centre. As a corollary, the following automatic continuity proposition is obtained for locally bounded finite-dimensional representations of connected locally compact groups: if G is a connected locally compact group, N is a compact normal subgroup of G such that the quotient group G/N is a Lie group, N{sub 0} is the connected identity component in N, H is the family of elements of G commuting with every element of N{sub 0}, and π is a (not necessarily continuous) locally bounded finite-dimensional representation of G, then π is continuous on the commutator subgroup of H (in the intrinsic topology of the smallest analytic subgroup of G containing this commutator subgroup). Bibliography: 23 titles. (paper)

Moscow State University, Research Institute for Systems Studies, Russian Academy of Sciences, Moscow (Russian Federation)

Publication Date:

OSTI Identifier:

22365293

Resource Type:

Journal Article

Resource Relation:

Journal Name: Sbornik. Mathematics; Journal Volume: 205; Journal Issue: 4; Other Information: Country of input: International Atomic Energy Agency (IAEA)