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Sinopsis
In this compact and succinct text, Kaplansky describes the resolution of Hilbert's fifth problem, that all locally Euclidean groups are Lie groups. Kaplansky analyses the problem itself with extensive exposition of the solution. He begins by describing Lie algebrae, including solvable and nilpotent algebrae, Cartan subalgebrae, and transitions to geometric problems. He then describes the structure of locally compact groups, including the existence of one-parameter subgroups, differentiable functions, functions constructed from a single Q or a sequence, proof that K is in a neighborhood of 1, and approximation by NSS groups. This was originally published by the U. of Chicago Press in 1971. Annotation ©2004 Book News, Inc., Portland, OR (booknews.com)
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Reseña del editor
In this compact and succinct text, Kaplansky describes the resolution of Hilbert's fifth problem, that all locally Euclidean groups are Lie groups. Kaplansky analyses the problem itself with extensive exposition of the solution. He begins by describing Lie algebrae, including solvable and nilpotent algebrae, Cartan subalgebrae, and transitions to geometric problems. He then describes the structure of locally compact groups, including the existence of one-parameter subgroups, differentiable functions, functions constructed from a single Q or a sequence, proof that K is in a neighborhood of 1, and approximation by NSS groups. This was originally published by the U. of Chicago Press in 1971. Annotation ©2004 Book News, Inc., Portland, OR (booknews.com)
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