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277097d · Aug 13, 2022

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The pin group and the spin group

In this file we define lipschitz consisting all the elements in (clifford_algebra)ˣ closed under conjugation and construct pin_group based on lipschitz and unitary, and we construct spin_group based on pin_group and clifford_algebra.even. Also, we show pin_group and spin_group form a group where the inverse is star.

Main definitions

  • lipschitz: the Lipschitz group with a quadratic form.
  • pin_group: the Pin group with a quadratic form.
  • spin_group: the Spin group with a quadratic form.

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