This is a graduate-level text that systematically develops the foundations of the subject. Quantum groups (i.e. Hopf algebras) are treated as mathematical objects in their own right; basic properties and theorems are proven in detail from this standpoint, including the results underlying key applications. After formal definitions and basic theory, the book goes on to cover such topics as quantum enveloping algebras, matrix quantum groups, combinatorics, cross products of various kinds, the quantum double, the semiclassical theory of Poisson-Lie groups, the representation theory, braided groups and applications to q-deformed physics. The explicit proofs and a great many worked examples and exercises will allow readers to quickly pick up the techniques needed for working in this exciting new field.
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"...this is a remarkable book, written in a rigorous style (all necessary statements are proved explicitly) by an acknowledged leader in the field." Dmitrii I. Gurevich, Mathematical Reviews
Book Description
This is a graduate-level text that systematically develops the foundations of the subject. Quantum groups (i.e. Hopf algebras) are treated as mathematical objects in their own right; basic properties and theorems are proven in detail from this standpoint, including the results underlying key applications. After formal definitions and the basic theory, the book goes on to cover such topics as quantum enveloping algebras, matrix quantum groups, combinatorics, cross products of various kinds, the quantum double, the semiclassical theory of Poisson-Lie groups, the representation theory, braided groups and applications to q-deformed physics. The explicit proofs and many worked examples and exercises will allow readers to quickly pick up the techniques needed for working in this exciting new field.
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Inside This Book
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First Sentence:
Here we collect the definitions and basic constructions that will be needed throughout the book. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
quasitriangular structure, quantum adjoint action, cross coproduct, quasitriangular bialgebra, braided coproduct, antialgebra map, bicrossproduct models, braided groups, cross product algebra, product coalgebra structure, right adjoint coaction, braided differentiation, double bosonisation, two bialgebras, anticoalgebra map, braided category, factorisable case, linear coproduct, right coaction, matched pair conditions, anyonic vector spaces, cocycle cross product, mutual coadjoint actions, covariant algebras, dual quasitriangular Key Phrases - Capitalized Phrases (CAPs): (learn more)
Hopf-von Neumann, Mac Lane New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Here we collect the definitions and basic constructions that will be needed throughout the book. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
quasitriangular structure, quantum adjoint action, cross coproduct, quasitriangular bialgebra, braided coproduct, antialgebra map, bicrossproduct models, braided groups, cross product algebra, product coalgebra structure, right adjoint coaction, braided differentiation, double bosonisation, two bialgebras, anticoalgebra map, braided category, factorisable case, linear coproduct, right coaction, matched pair conditions, anyonic vector spaces, cocycle cross product, mutual coadjoint actions, covariant algebras, dual quasitriangular Key Phrases - Capitalized Phrases (CAPs): (learn more)
Hopf-von Neumann, Mac Lane New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 12
books:
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25
books
cite this book:
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- Quantum Probability and Related Topics by L. Accardi in Back Matter (1), and Back Matter (2)
- Quantum Groups, Integrable Statistical Models and Knot Theory (Nankai Lectures on Mathematical Physics) by H. J. De Vega in Back Matter
- Quantum Symmetries on Operator Algebras (Oxford Mathematical Monographs) by David E. Evans in Back Matter
- Hopf Algebras (Math Lecture Notes, No 44) by Moss E. Sweedler in Back Matter
- An Introduction to Quantum Stochastic Calculus by K. R. Parthasarathy in Back Matter
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- Quantum Groups and Lie Theory (London Mathematical Society Lecture Note Series) by Andrew Pressley on page 30, and page 188
- Quantum Groups: A Path to Current Algebra (Australian Mathematical Society Lecture Series) by Ross Street in Front Matter, and Back Matter
- Clifford Algebras: Applications to Mathematics, Physics, and Engineering (Progress in Mathematical Physics, Vol. 34) by Rafal Ablamowicz on page 303, and page 517
- Clifford Algebras and their Applications in Mathematical Physics, Vol.1: Algebra and Physics by Rafal Ablamowicz on page 267, and page 365
- Hopf Algebras in Noncommutative Geometry and Physics (Lecture Notes in Pure and Applied Mathematics) by Stefaan Caenepeel on page 187, and page 213
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