# Division algebra valued energized simplicial complexes

@article{Knill2020DivisionAV, title={Division algebra valued energized simplicial complexes}, author={Oliver Knill}, journal={arXiv: Mathematical Physics}, year={2020} }

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…

## One Citation

Graph complements of circular graphs

- MathematicsArXiv
- 2021

There is now a non-trivial 6-periodic Gauss-Bonnet curvature universality in the complement of Barycentric limits, which produces a 12-periodicity of the Lefschetz numbers of all graph automorphisms of Gn.

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