geometric conceptions of groups (and walks of graphs from groups); Heisenberg group


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http://terrytao.wordpress.com/2010/07/10/cayley-graphs-and-the-geometry-of-groups/

In Turing’s case, his ei=(-1)  or ei=(+1) are ei=(-1…-d)  or ei=(+1…+d) – since he is thinking in qudits rather than qubits.

The Heisenburg group, properly explained, also makes clear how metrics can differ – by generating set choice (and therefore degree of the graph).

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Geometric Aspects of the Heisenberg Group

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