A Quaternionic Construction of E7
نویسنده
چکیده
We give an explicit construction of the simply-connected compact real form of the Lie group of type E7, as a group of 28 × 28 matrices over quaternions, acting on a 28-dimensional left quaternion vector space. This leads to a description of the simply-connected split real form, acting on a 56dimensional real vector space, and thence to the finite quasi-simple groups of type E7. The sign problems usually associated with constructing exceptional Lie groups are almost entirely absent from this approach.
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