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Cayley 4-frames and a quaternion-Kähler reduction related to Spin(7)

Liviu Ornea·Paolo Piccinni
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Abstract

We describe an action of $U(1)\times Sp(1)$ on $HP^7$ that allows to obtain a $Z_2$-quotient of CAYLEY (the Grassmannian of oriented 4-planes in $R^8$ closed under the three-fold cross product) by quaternionic Kähler reduction.

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Liviu Ornea, Paolo Piccinni. 2001-06-13. Cayley 4-frames and a quaternion-Kähler reduction related to Spin(7). https://arxiv.org/abs/math/0106116

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