Noncommutative solutions to the local tetrahedron equation
We study the solutions of the local Zamolodchikov tetrahedron equation on noncommutative groups and division rings in the form of correspondences derived from 3 × 3 matrices with free noncommutative variables. The complete set of generators for 4-simplex maps that adhere to the local tetrahedron equ...
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| Format: | Article |
| Language: | English |
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Elsevier
2024-12-01
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| Series: | Partial Differential Equations in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818124003541 |
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| author | M. Chirkov |
| author_facet | M. Chirkov |
| author_sort | M. Chirkov |
| collection | DOAJ |
| description | We study the solutions of the local Zamolodchikov tetrahedron equation on noncommutative groups and division rings in the form of correspondences derived from 3 × 3 matrices with free noncommutative variables. The complete set of generators for 4-simplex maps that adhere to the local tetrahedron equation is presented. We study the difference in classification between commutative and noncommutative cases. Additionally, we introduce a procedure for obtaining novel 4-simplex maps associated with known tetrahedron maps. Also, we introduce the “conditional n-simplex maps” and study the case of 4-simplex maps via examples. Lastly, several new 4-simplex maps on noncommutative groups are constructed. |
| format | Article |
| id | doaj-art-35c7ac6d05624e9291462697754b8e18 |
| institution | Kabale University |
| issn | 2666-8181 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj-art-35c7ac6d05624e9291462697754b8e182024-12-13T11:05:46ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812024-12-0112100968Noncommutative solutions to the local tetrahedron equationM. Chirkov0P.G. Demidov Yaroslavl State University, Yaroslavl, Russia, HSE University, Moscow, RussiaWe study the solutions of the local Zamolodchikov tetrahedron equation on noncommutative groups and division rings in the form of correspondences derived from 3 × 3 matrices with free noncommutative variables. The complete set of generators for 4-simplex maps that adhere to the local tetrahedron equation is presented. We study the difference in classification between commutative and noncommutative cases. Additionally, we introduce a procedure for obtaining novel 4-simplex maps associated with known tetrahedron maps. Also, we introduce the “conditional n-simplex maps” and study the case of 4-simplex maps via examples. Lastly, several new 4-simplex maps on noncommutative groups are constructed.http://www.sciencedirect.com/science/article/pii/S2666818124003541n-simplex mapsTetrahedron mapsLocal Zamolodchikov tetrahedron equationYang–Baxter mapsDivision ringsConditional n-simplex maps |
| spellingShingle | M. Chirkov Noncommutative solutions to the local tetrahedron equation Partial Differential Equations in Applied Mathematics n-simplex maps Tetrahedron maps Local Zamolodchikov tetrahedron equation Yang–Baxter maps Division rings Conditional n-simplex maps |
| title | Noncommutative solutions to the local tetrahedron equation |
| title_full | Noncommutative solutions to the local tetrahedron equation |
| title_fullStr | Noncommutative solutions to the local tetrahedron equation |
| title_full_unstemmed | Noncommutative solutions to the local tetrahedron equation |
| title_short | Noncommutative solutions to the local tetrahedron equation |
| title_sort | noncommutative solutions to the local tetrahedron equation |
| topic | n-simplex maps Tetrahedron maps Local Zamolodchikov tetrahedron equation Yang–Baxter maps Division rings Conditional n-simplex maps |
| url | http://www.sciencedirect.com/science/article/pii/S2666818124003541 |
| work_keys_str_mv | AT mchirkov noncommutativesolutionstothelocaltetrahedronequation |