Hopf Algebras, Quantum Groups and Yang-Baxter Equations
The Yang-Baxter equation first appeared in theoretical physics, in a paper by the Nobel laureate C.N. Yang and in the work of R.J. Baxter in the field of Statistical Mechanics. At the 1990 International Mathematics Congress, Vladimir Drinfeld, Vaughan F. R. Jones, and Edward Witten were awarded Fiel...
Saved in:
| Hovedforfatter: | |
|---|---|
| Format: | Online |
| Sprog: | engelsk |
| Udgivet: |
MDPI - Multidisciplinary Digital Publishing Institute
2021
|
| Fag: | |
| Online adgang: | 32127 |
| Tags: |
Ingen Tags, Vær først til at tagge denne postø!
|
| _version_ | 1869528632985124864 |
|---|---|
| author | Florin Felix Nichita (Ed.) |
| author_browse | Florin Felix Nichita (Ed.) |
| author_facet | Florin Felix Nichita (Ed.) |
| author_sort | Florin Felix Nichita (Ed.) |
| collection | Directory of Open Access Books |
| description | The Yang-Baxter equation first appeared in theoretical physics, in a paper by the Nobel laureate C.N. Yang and in the work of R.J. Baxter in the field of Statistical Mechanics. At the 1990 International Mathematics Congress, Vladimir Drinfeld, Vaughan F. R. Jones, and Edward Witten were awarded Fields Medals for their work related to the Yang-Baxter equation. It turned out that this equation is one of the basic equations in mathematical physics; more precisely, it is used for introducing the theory of quantum groups. It also plays a crucial role in: knot theory, braided categories, the analysis of integrable systems, non-commutative descent theory, quantum computing, non-commutative geometry, etc. Many scientists have used the axioms of various algebraic structures (quasi-triangular Hopf algebras, Yetter-Drinfeld categories, quandles, group actions, Lie (super)algebras, brace structures, (co)algebra structures, Jordan triples, Boolean algebras, relations on sets, etc.) or computer calculations (and Grobner bases) in order to produce solutions for the Yang-Baxter equation. However, the full classification of its solutions remains an open problem. At present, the study of solutions of the Yang-Baxter equation attracts the attention of a broad circle of scientists. The current volume highlights various aspects of the Yang-Baxter equation, related algebraic structures, and applications. |
| format | Online |
| id | doab-20.500.12854ir-49556 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2021 |
| publishDateRange | 2021 |
| publishDateSort | 2021 |
| publisher | MDPI - Multidisciplinary Digital Publishing Institute |
| publisherStr | MDPI - Multidisciplinary Digital Publishing Institute |
| record_format | ojs |
| spelling | doab-20.500.12854ir-495562023-12-20T18:40:40Z Hopf Algebras, Quantum Groups and Yang-Baxter Equations Florin Felix Nichita (Ed.) QA1-939 QC1-999 braided category quasitriangular structure quantum projective space Hopf algebra quantum integrability duality six-vertex model Quantum Group Yang-Baxter equation star-triangle relation R-matrix Lie algebra bundle braid group bic Book Industry Communication::P Mathematics & science The Yang-Baxter equation first appeared in theoretical physics, in a paper by the Nobel laureate C.N. Yang and in the work of R.J. Baxter in the field of Statistical Mechanics. At the 1990 International Mathematics Congress, Vladimir Drinfeld, Vaughan F. R. Jones, and Edward Witten were awarded Fields Medals for their work related to the Yang-Baxter equation. It turned out that this equation is one of the basic equations in mathematical physics; more precisely, it is used for introducing the theory of quantum groups. It also plays a crucial role in: knot theory, braided categories, the analysis of integrable systems, non-commutative descent theory, quantum computing, non-commutative geometry, etc. Many scientists have used the axioms of various algebraic structures (quasi-triangular Hopf algebras, Yetter-Drinfeld categories, quandles, group actions, Lie (super)algebras, brace structures, (co)algebra structures, Jordan triples, Boolean algebras, relations on sets, etc.) or computer calculations (and Grobner bases) in order to produce solutions for the Yang-Baxter equation. However, the full classification of its solutions remains an open problem. At present, the study of solutions of the Yang-Baxter equation attracts the attention of a broad circle of scientists. The current volume highlights various aspects of the Yang-Baxter equation, related algebraic structures, and applications. 2021-02-11T15:32:29Z 2021-02-11T15:32:29Z 2019-01-31 11:04:50 2019 book 32127 9783038973256 9783038973249 https://directory.doabooks.org/handle/20.500.12854/49556 eng image/jpeg Attribution-NonCommercial-NoDerivatives 4.0 International https://www.mdpi.com/books/pdfview/book/1119 https://play.google.com/books/publish/a/14935057684283403269#details/ISBN:9783038973249 https://www.mdpi.com/books/pdfview/book/1119 MDPI - Multidisciplinary Digital Publishing Institute 10.3390/books978-3-03897-325-6 10.3390/books978-3-03897-325-6 46cabcaa-dd94-4bfe-87b4-55023c1b36d0 9783038973256 9783038973249 238 open access |
| spellingShingle | QA1-939 QC1-999 braided category quasitriangular structure quantum projective space Hopf algebra quantum integrability duality six-vertex model Quantum Group Yang-Baxter equation star-triangle relation R-matrix Lie algebra bundle braid group bic Book Industry Communication::P Mathematics & science Florin Felix Nichita (Ed.) Hopf Algebras, Quantum Groups and Yang-Baxter Equations |
| title | Hopf Algebras, Quantum Groups and Yang-Baxter Equations |
| title_full | Hopf Algebras, Quantum Groups and Yang-Baxter Equations |
| title_fullStr | Hopf Algebras, Quantum Groups and Yang-Baxter Equations |
| title_full_unstemmed | Hopf Algebras, Quantum Groups and Yang-Baxter Equations |
| title_short | Hopf Algebras, Quantum Groups and Yang-Baxter Equations |
| title_sort | hopf algebras quantum groups and yang baxter equations |
| topic | QA1-939 QC1-999 braided category quasitriangular structure quantum projective space Hopf algebra quantum integrability duality six-vertex model Quantum Group Yang-Baxter equation star-triangle relation R-matrix Lie algebra bundle braid group bic Book Industry Communication::P Mathematics & science |
| topic_facet | QA1-939 QC1-999 braided category quasitriangular structure quantum projective space Hopf algebra quantum integrability duality six-vertex model Quantum Group Yang-Baxter equation star-triangle relation R-matrix Lie algebra bundle braid group bic Book Industry Communication::P Mathematics & science |
| url | 32127 |
| work_keys_str_mv | AT florinfelixnichitaed hopfalgebrasquantumgroupsandyangbaxterequations |