Universal observability and codimension one subgroups of Borel subgroups
نویسندگان
چکیده
منابع مشابه
Borel Subgroups of Polish Groups
We study three classes of subgroups of Polish groups: Borel subgroups, Polishable subgroups, and maximal divisible subgroups. The membership of a subgroup in each of these classes allows one to assign to it a rank, that is, a countable ordinal, measuring in a natural way complexity of the subgroup. We prove theorems comparing these three ranks and construct subgroups with prescribed ranks. In p...
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We demonstrate a relationships between the representation theory of Borel subgroups and parabolic subgroups of general linear groups. In particular, we show that the representations of Borel subgroups could be computed from representations of certain maximal parabolic subgroups.
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Given a class C of subgroups of a topological group G, we say that a subgroup H ∈ C is a universal C subgroup of G if every subgroup K ∈ C is a continuous homomorphic pre-image of H. Such subgroups may be regarded as complete members of C with respect to a natural pre-order on the set of subgroups of G. We show that for any locally compact Polish group G, the countable power G has a universal K...
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Let k be an algebraically closed field. Let B be the Borel subgroup of GLn(k) consisting of nonsingular upper triangular matrices. Let b = LieB be the Lie algebra of upper triangular n × n matrices and u the Lie subalgebra of b consisting of strictly upper triangular matrices. We classify all Lie ideals n of b, satisfying u ⊆ n ⊆ u, such that B acts (by conjugation) on n with a dense orbit. Fur...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1985
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1985.120.215