• Corpus ID: 221266494

Division algebra valued energized simplicial complexes

  title={Division algebra valued energized simplicial complexes},
  author={Oliver Knill},
  journal={arXiv: Mathematical Physics},
  • O. Knill
  • Published 24 August 2020
  • Mathematics
  • arXiv: Mathematical Physics
We look at connection Laplacians L,g defined by a field h:G to K, where G is a finite set of sets and K is a normed division ring which does not need to be commutative, nor associative but has a conjugation leading to the norm as the square root of h^* h. The target space K can be a normed real division algebra like the quaternions or an algebraic number field like a quadratic field. For parts of the results we can even assume K to be a Banach algebra like an operator algebra on a Hilbert space… 

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