{"product_id":"quantum-groups-in-three-dimensional-integrability-hardcover","title":"Quantum Groups in Three-Dimensional Integrability - Hardcover","description":"\u003cp\u003eby \u003cb\u003eAtsuo Kuniba\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003eQuantum groups have been studied intensively in mathematics and have found many valuable applications in theoretical and mathematical physics since their discovery in the mid-1980s. Roughly speaking, there are two prototype examples of quantum groups, denoted by \u003ci\u003eU\u003csub\u003eq\u003c\/sub\u003e\u003c\/i\u003e and \u003ci\u003eA\u003csub\u003eq\u003c\/sub\u003e\u003c\/i\u003e. The former is a deformation of the universal enveloping algebra of a Kac-Moody Lie algebra, whereas the latter is a deformation of the coordinate ring of a Lie group. Although they are dual to each other in principle, most of the applications so far are based on \u003ci\u003eU\u003csub\u003eq\u003c\/sub\u003e\u003c\/i\u003e, and the main targets are solvable lattice models in 2-dimensions or quantum field theories in 1+1 dimensions. This book aims to present a unique approach to 3-dimensional integrability based on \u003ci\u003eA\u003csub\u003eq\u003c\/sub\u003e\u003c\/i\u003e. It starts from the tetrahedron equation, a 3-dimensional analogue of the Yang-Baxter equation, and its solution due to work by Kapranov-Voevodsky (1994). Then, it guides readers to its variety of generalizations, relations to quantum groups, and applications. They include a connection to the Poincaré-Birkhoff-Witt basis of a unipotent part of \u003ci\u003eU\u003csub\u003eq\u003c\/sub\u003e\u003c\/i\u003e, reductions to the solutions of the Yang-Baxter equation, reflection equation, \u003ci\u003eG\u003c\/i\u003e\u003csub\u003e2\u003c\/sub\u003e reflection equation, matrix product constructions of quantum R matrices and reflection K matrices, stationary measures of multi-species simple-exclusion processes, etc. These contents of the book are quite distinct from conventional approaches and will stimulate and enrich the theories of quantum groups and integrable systems. \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003ch3\u003eBack Jacket\u003c\/h3\u003e\u003cp\u003eQuantum groups have been studied intensively in mathematics and have found many valuable applications in theoretical and mathematical physics since their discovery in the mid-1980s. Roughly speaking, there are two prototype examples of quantum groups, denoted by \u003ci\u003eU\u003csub\u003eq\u003c\/sub\u003e\u003c\/i\u003e and \u003ci\u003eA\u003csub\u003eq\u003c\/sub\u003e\u003c\/i\u003e. The former is a deformation of the universal enveloping algebra of a Kac-Moody Lie algebra, whereas the latter is a deformation of the coordinate ring of a Lie group. Although they are dual to each other in principle, most of the applications so far are based on \u003ci\u003eU\u003csub\u003eq\u003c\/sub\u003e\u003c\/i\u003e, and the main targets are solvable lattice models in 2-dimensions or quantum field theories in 1+1 dimensions. This book aims to present a unique approach to 3-dimensional integrability based on \u003ci\u003eA\u003csub\u003eq\u003c\/sub\u003e\u003c\/i\u003e. It starts from the tetrahedron equation, a 3-dimensional analogue of the Yang-Baxter equation, and its solution due to work by Kapranov-Voevodsky (1994). Then, it guides readers to its variety of generalizations, relations to quantum groups, and applications. They include a connection to the Poincaré-Birkhoff-Witt basis of a unipotent part of \u003ci\u003eU\u003csub\u003eq\u003c\/sub\u003e\u003c\/i\u003e, reductions to the solutions of the Yang-Baxter equation, reflection equation, \u003ci\u003eG\u003c\/i\u003e\u003csub\u003e2\u003c\/sub\u003e reflection equation, matrix product constructions of quantum R matrices and reflection K matrices, stationary measures of multi-species simple-exclusion processes, etc. These contents of the book are quite distinct from conventional approaches and will stimulate and enrich the theories of quantum groups and integrable systems.\u003cbr\u003e\u003c\/p\u003e\u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 331\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 0.81 x 9.21 x 6.14 IN\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003eIllustrated:\u003c\/strong\u003e Yes\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e September 26, 2022\u003c\/div\u003e","brand":"Books by splitShops","offers":[{"title":"Default Title","offer_id":42718766334015,"sku":"9789811932618","price":213.82,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0105\/8226\/1823\/files\/ce679e57f808560bf568793d81c6a1a7.webp?v=1765083176","url":"https:\/\/dhlswag.com\/products\/quantum-groups-in-three-dimensional-integrability-hardcover","provider":"BBB","version":"1.0","type":"link"}