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Maximal Protori in Compact Topological Groups
Author(s) -
AHDOUT SHAHLA,
HURWITZ CAROL,
ITZKOWITZ GERALD,
ROTHMAN SHELDON,
STRASSBERG HELEN
Publication year - 1994
Publication title -
annals of the new york academy of sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.712
H-Index - 248
eISSN - 1749-6632
pISSN - 0077-8923
DOI - 10.1111/j.1749-6632.1994.tb44147.x
Subject(s) - maximal torus , mathematics , torus , lie group , abelian group , topological group , topology (electrical circuits) , direct limit , compact group , limit (mathematics) , pure mathematics , combinatorics , discrete mathematics , mathematical analysis , geometry , lie algebra , fundamental representation , weight
The analysis of Lie groups depends to a large extent on their maximal tori. For a compact connected topological group G , the subgroups analogous to the maximal tori are the maximal connected Abelian subgroups. As in Hofmann and Morris [7] we call them maximal protori. We sharpen some results of [7] by showing that each maximal protorus is in a natural way the projective limit of maximal tori T α in the corresponding G α , where G = proj G α . This sharpened characterization together with some methods of Moskowitz [4], [10] will be used to show that a number of well‐known theorems concerning Lie groups extend in a natural way to all compact connected groups.