Cohomologies of $n$-simplex relations
Mathematical Physics
2016-05-23 v3 Algebraic Topology
math.MP
Quantum Algebra
Abstract
A theory of (co)homologies related to set-theoretic -simplex relations is constructed in analogy with the known quandle and Yang--Baxter (co)homologies, with emphasis made on the tetrahedron case. In particular, this permits us to generalize Hietarinta's idea of "permutation-type" solutions to the quantum (or "tensor") -simplex equations. Explicit examples of solutions to the tetrahedron equation involving nontrivial cocycles are presented.
Keywords
Cite
@article{arxiv.1409.3127,
title = {Cohomologies of $n$-simplex relations},
author = {Igor Korepanov and Georgy Sharygin and Dmitry Talalaev},
journal= {arXiv preprint arXiv:1409.3127},
year = {2016}
}
Comments
25 pages, 4 figures; v3: added the proof of nontriviality in Example 2, formulas in this example corrected