{"product_id":"quantum-groups-in-three-dimensional-integrability-9789811932649","title":"Quantum Groups in Three-Dimensional Integrability","description":"Quantum 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. \u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Atsuo Kuniba\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Springer\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 09\/27\/2023\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 331\u003cbr\u003e\u003cb\u003eBinding Type:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 1.06lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.21h x 6.14w x 0.72d\u003cbr\u003e\u003cb\u003eISBN:\u003c\/b\u003e 9789811932649","brand":"Springer","offers":[{"title":"Paperback","offer_id":43027416744051,"sku":"9.78981E+12","price":186.77,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0555\/9255\/0515\/files\/img_aa8b38ba-ebd5-444c-9d59-ae0647059981.jpg?v=1746029978","url":"https:\/\/bookstorenmore.com\/products\/quantum-groups-in-three-dimensional-integrability-9789811932649","provider":"Bookstore N More","version":"1.0","type":"link"}