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libcats.org
On Quaternions and OctonionsJohn Horton Conway, Derek SmithThis books gives a window into the newer notation in group theory.
Sometimes things that are "obvious" to Conway and his co-arthor, just aren't to the rest of us. But in contrast to that he gives concrete examples of new approaches that are beyond classical Coexter and Cartan type approaches. If you are looking for physics applications to quantum mechanics for modern group theory, you might want to try another book, but if you want an idea of what a Moufang loop is or why octonions are not associative, then you might like this book. Some time in this century we may even get a chance to understand Freudenthal's metasymplectic geometry? This book for me is sort of a study guide to what i should try to learn for the future?
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