Introduction to Quantum Groups and Crystal Bases (Graduate Studies in Mathematics)

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9780821828748: Introduction to Quantum Groups and Crystal Bases (Graduate Studies in Mathematics)

The notion of a 'quantum group' was introduced by V.G. Dinfeld and M. Jimbo, independently, in their study of the quantum Yang-Baxter equation arising from 2-dimensional solvable lattice models. Quantum groups are certain families of Hopf algebras that are deformations of universal enveloping algebras of Kac-Moody algebras. And over the past 20 years, they have turned out to be the fundamental algebraic structure behind many branches of mathematics and mathematical physics, such as solvable lattice models in statistical mechanics, topological invariant theory of links and knots, representation theory of Kac-Moody algebras, representation theory of algebraic structures, topological quantum field theory, geometric representation theory, and $C^*$-algebras. In particular, the theory of 'crystal bases' or 'canonical bases' developed independently by M. Kashiwara and G. Lusztig provides a powerful combinatorial and geometric tool to study the representations of quantum groups.The purpose of this book is to provide an elementary introduction to the theory of quantum groups and crystal bases, focusing on the combinatorial aspects of the theory.

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Jin Hong; Seok-Jin Kang
Edité par American Mathematical Society (2002)
ISBN 10 : 0821828746 ISBN 13 : 9780821828748
Neuf(s) Couverture rigide Quantité : > 20
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Description du livre American Mathematical Society, 2002. Hardcover. État : New. Brand new. We distribute directly for the publisher. The notion of a "quantum group" was introduced by V.G. Dinfeld́ and M. Jimbo, independently, in their study of the quantum Yang-Baxter equation arising from 2-dimensional solvable lattice models. Quantum groups are certain families of Hopf algebras that are deformations of universal enveloping algebras of Kac-Moody algebras. And over the past 20 years, they have turned out to be the fundamental algebraic structure behind many branches of mathematics and mathematical physics, such as solvable lattice models in statistical mechanics, topological invariant theory of links and knots, representation theory of Kac-Moody algebras, representation theory of algebraic structures, topological quantum field theory, geometric representation theory, and $C^*$-algebras.In particular, the theory of "crystal bases" or "canonical bases" developed independently by M. Kashiwara and G. Lusztig provides a powerful combinatorial and geometric tool to study the representations of quantum groups. The purpose of this book is to provide an elementary introduction to the theory of quantum groups and crystal bases, focusing on the combinatorial aspects of the theory. N° de réf. du libraire 1005120070

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Jin Hong, Seok-Jin Kang
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ISBN 10 : 0821828746 ISBN 13 : 9780821828748
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Description du livre American Mathematical Society, United States, 2002. Hardback. État : New. Language: English . Brand New Book. The notion of a quantum group was introduced by V.G. Dinfeld and M. Jimbo, independently, in their study of the quantum Yang-Baxter equation arising from 2-dimensional solvable lattice models. Quantum groups are certain families of Hopf algebras that are deformations of universal enveloping algebras of Kac-Moody algebras. And over the past 20 years, they have turned out to be the fundamental algebraic structure behind many branches of mathematics and mathematical physics, such as solvable lattice models in statistical mechanics, topological invariant theory of links and knots, representation theory of Kac-Moody algebras, representation theory of algebraic structures, topological quantum field theory, geometric representation theory, and $C^*$-algebras. In particular, the theory of crystal bases or canonical bases developed independently by M. Kashiwara and G. Lusztig provides a powerful combinatorial and geometric tool to study the representations of quantum groups.The purpose of this book is to provide an elementary introduction to the theory of quantum groups and crystal bases, focusing on the combinatorial aspects of the theory. N° de réf. du libraire AAN9780821828748

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Jin Hong, Seok-Jin Kang
Edité par American Mathematical Society, United States (2002)
ISBN 10 : 0821828746 ISBN 13 : 9780821828748
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Description du livre American Mathematical Society, United States, 2002. Hardback. État : New. Language: English . Brand New Book. The notion of a quantum group was introduced by V.G. Dinfeld and M. Jimbo, independently, in their study of the quantum Yang-Baxter equation arising from 2-dimensional solvable lattice models. Quantum groups are certain families of Hopf algebras that are deformations of universal enveloping algebras of Kac-Moody algebras. And over the past 20 years, they have turned out to be the fundamental algebraic structure behind many branches of mathematics and mathematical physics, such as solvable lattice models in statistical mechanics, topological invariant theory of links and knots, representation theory of Kac-Moody algebras, representation theory of algebraic structures, topological quantum field theory, geometric representation theory, and $C^*$-algebras. In particular, the theory of crystal bases or canonical bases developed independently by M. Kashiwara and G. Lusztig provides a powerful combinatorial and geometric tool to study the representations of quantum groups.The purpose of this book is to provide an elementary introduction to the theory of quantum groups and crystal bases, focusing on the combinatorial aspects of the theory. N° de réf. du libraire AAN9780821828748

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Description du livre Amer Mathematical Society. Hardcover. État : New. 0821828746 Satisfaction Guaranteed. Please contact us with any inquiries. We ship daily. N° de réf. du libraire Z0821828746ZN

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Description du livre American Mathematical Society, 2002. HRD. État : New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. N° de réf. du libraire CE-9780821828748

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Description du livre American Mathematical Society. Hardback. État : new. BRAND NEW, Introduction to Quantum Groups and Crystal Bases, Jin Hong, Seok-Jin Kang, The notion of a 'quantum group' was introduced by V.G. Dinfeld and M. Jimbo, independently, in their study of the quantum Yang-Baxter equation arising from 2-dimensional solvable lattice models. Quantum groups are certain families of Hopf algebras that are deformations of universal enveloping algebras of Kac-Moody algebras. And over the past 20 years, they have turned out to be the fundamental algebraic structure behind many branches of mathematics and mathematical physics, such as solvable lattice models in statistical mechanics, topological invariant theory of links and knots, representation theory of Kac-Moody algebras, representation theory of algebraic structures, topological quantum field theory, geometric representation theory, and $C^*$-algebras. In particular, the theory of 'crystal bases' or 'canonical bases' developed independently by M. Kashiwara and G. Lusztig provides a powerful combinatorial and geometric tool to study the representations of quantum groups.The purpose of this book is to provide an elementary introduction to the theory of quantum groups and crystal bases, focusing on the combinatorial aspects of the theory. N° de réf. du libraire B9780821828748

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