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| | Weyl Groups |
 | | Since 3 is the dimension of the imaginary quaternions, Spin(0,3) has quaternionic structure and in fact generates the Lie group S3 of imaginary quaternions, and corresponds to the Associative Triangle of Imaginary Quaternions. |
 | | (0,-1) Here WEYL is the root vector space of Spin(0,4) in which reflections through the origin (0,0) act on the first axis to interchange (-1,0) and (+1,0) and on the second axis to interchange (0,-1) and (0,+1). |
 | | This type of construction can be continued to form the Weyl groups of all the B and D Lie algebras, and similar constructions can be used for the A, C, and Exceptional Lie algebras. |
| www.valdostamuseum.org /hamsmith/WeyLie.html (3488 words) |
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