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20 January 2020
  » arxiv » nlin.SI/0003024

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A formula with hypervolumes of six 4-simplices and two discrete curvatures
I.G. Korepanov ;
Date 10 Mar 2000
Subject Exactly Solvable and Integrable Systems; Metric Geometry; Quantum Algebra | nlin.SI gr-qc hep-lat math.MG math.QA
AbstractOne of the generalizations of the pentagon equation to higher dimensions is the so-called "six-term equation". Geometrically, it corresponds to one of the "Alexander moves", that is elementary rebuildings of simplicial complexes, namely, replacing a "cluster" of three 4-simplices by another "cluster", also of three 4-simplices and with the same boundary. We present a formula containing the euclidean volumes of the simplices in the first cluster in its l.h.s., and those in the second cluster - in its r.h.s. The formula also involves "discrete curvatures" appearing when we slightly deform the euclidean space.
Source arXiv, nlin.SI/0003024
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