{"product_id":"9789811932618","title":"Theoretical and Mathematical Physics","description":"\u003ch1\u003eTheoretical and Mathematical Physics\u003c\/h1\u003e \u003ch2\u003eKuniba, Atsuo\u003c\/h2\u003e \u003cp\u003e\u003c\/p\u003e\u003cdiv\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.\u003c\/div\u003e\u003cdiv\u003e \u003c\/div\u003e\u003cdiv\u003eThis 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).\u003c\/div\u003e\u003cdiv\u003e \u003c\/div\u003e\u003cdiv\u003eThen, 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.\u003c\/div\u003e\u003cdiv\u003e \u003c\/div\u003e\u003cdiv\u003eThese contents of the book are quite distinct from conventional approaches and will stimulate and enrich the theories of quantum groups and integrable systems.\u003c\/div\u003e\u003cdiv\u003e\n\u003cbr\u003e\u003cbr\u003e\n\u003c\/div\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2022-09-26\u003c\/p\u003e \u003cp\u003eFormat: Hardcover\u003c\/p\u003e \u003cp\u003eISBN-13: 9789811932618\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-981-19-3262-5\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 331\u003c\/p\u003e ","brand":"Springer Nature Singapore","offers":[{"title":"Default Title","offer_id":44806397198476,"sku":"9789811932618","price":98.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9789811932618.jpg?v=1776437527","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9789811932618","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}