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Yangians and Classical Lie Algebras (Mathematical Surveys and Monographs)
Alexander Molev
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Description for Yangians and Classical Lie Algebras (Mathematical Surveys and Monographs)
Hardcover. The Yangians and twisted Yangians are remarkable associative algebras taking their origins from the work of St Petersburg's school of mathematical physics in the 1980s. The book gives an introduction to the theory of Yangians and twisted Yangians, with a particular emphasis on the relationship with the classical matrix Lie algebras. Series: Mathematical Surveys and Monographs. Num Pages: 400 pages. BIC Classification: PBF; PBV; PBW; PHQ. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly. Dimension: 262 x 183 x 26. Weight in Grams: 890.
The Yangians and twisted Yangians are remarkable associative algebras taking their origins from the work of St. Petersburg's school of mathematical physics in the 1980s. The general definitions were given in subsequent work of Drinfeld and Olshansky, and these algebras have since found numerous applications in and connections with mathematical physics, geometry, representation theory, and combinatorics. The book is an introduction to the theory of Yangians and twisted Yangians, with a particular emphasis on the relationship with the classical matrix Lie algebras. A special algebraic technique, the $R$-matrix formalism, is developed and used as the main instrument for describing the structure of Yangians. A detailed exposition of the highest weight theory and the classification theorems for finite-dimensional irreducible representations of these algebras is given. The Yangian perspective provides a unifying picture of several families of Casimir elements for the classical Lie algebras and relations between these families.The Yangian symmetries play a key role in explicit constructions of all finite-dimensional irreducible representations of the orthogonal and symplectic Lie algebras via weight bases of Gelfand-Tsetlin type.
Product Details
Format
Hardback
Publication date
2007
Publisher
American Mathematical Society
Condition
New
Series
Mathematical Surveys and Monographs
Number of Pages
400
Place of Publication
Providence, United States
ISBN
9780821843741
SKU
V9780821843741
Shipping Time
Usually ships in 7 to 11 working days
Ref
99-1
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