Report
Cohomologies of $n$-simplex relations
| العنوان: | Cohomologies of $n$-simplex relations |
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| المؤلفون: | Korepanov, Igor, Sharygin, Georgy, Talalaev, Dmitry |
| سنة النشر: | 2014 |
| المجموعة: | Mathematics Mathematical Physics |
| مصطلحات موضوعية: | Mathematical Physics, Mathematics - Algebraic Topology, Mathematics - Quantum Algebra |
| الوصف: | A theory of (co)homologies related to set-theoretic $n$-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") $n$-simplex equations. Explicit examples of solutions to the tetrahedron equation involving nontrivial cocycles are presented. Comment: 25 pages, 4 figures; v3: added the proof of nontriviality in Example 2, formulas in this example corrected |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1017/S030500411600030X |
| URL الوصول: | http://arxiv.org/abs/1409.3127 |
| رقم الانضمام: | edsarx.1409.3127 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1017/S030500411600030X |
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