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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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2024-12-01
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| Series: | Partial Differential Equations in Applied Mathematics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818124003541 |
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| Summary: | 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. |
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| ISSN: | 2666-8181 |