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QUANTUM GROUPS (M1,2, Majid)

Lecture Topic : (Math Physics)  QUANTUM  GROUPS  (M1,2, Majid)

Prerequisites : Finite Group Theory (Sen, M1); Category Theory (M2); Representation Theory (M1); Knot Theory (M1); Lie Algebras (M1);

Recommended Text(s) :

“A Quantum Groups Primer”, Shahn Majid,Cambridge University Press, 2002

Approx price new on Amazon.com (hard copy) : $63

Approx price second hand on Amazon.com (hard copy) : $60

Availability free on eMule.com (e-format) : Yes

eMule search key word(s) : “Quantum Groups Primer”, Majid

Lectures and Links :

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Lecture 1  (link)

Ch.1   Coalgebras, Bialgebras and Hopf Algebras  Uq(b+)

Ch.2   Dual Pairaing. SLq(2). Actions

Ch.3   Coactions. Quantum plane A2q

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Lecture 2  (link)

Ch.4   Automorphism Quantum Groups

Ch.5   Quasitriangular Structures

Ch.6   Roots of Unity. uq(sl2)

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Lecture 3  (link)

Ch.7   q-Binomials

Ch.8   Quantum Double. Dual-quasitriangular Structures

Ch.9   Braided Categories

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Lecture 4  (link)

Ch.10  (Co)module Categories. Crossed Modules

Ch.11   q-Hecke Algebras

Ch.12   Rigid Objects. Dual Representations. Quantum Dimension

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Lecture 5  (link)

Ch.13   Knot Invariants

Ch.14   Hopf Algebras in Braided Categories. Coaddition on A2q

Ch.15   Braided Differentiation

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Lecture 6  (link)

Ch.16   Bosonization. Inhomogeneous Quantum Groups

Ch.17   Double Bosonization. Diagrammatic Construction of uq(sl2)

Ch.18   The Braided Group Uq(n+). Construction of Uq(g)

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Lecture 7  (link)

Ch.19   q-Serre Relations

Ch.20   R-Matrix Methods

Ch.21   Group, Algebra, Hopf Algebra Factorizations. Bicrossproducts

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Lecture 8  (link)

Ch.22   Lie Bialgebras. Lie Splittings. Iwasawa Decomposition

Ch.23   Poisson Geometry. Noncommutative Bundles. Q-Sphere

Ch.24   Connections. Q-Monopole. Nonuniversal Differentials

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Links to Other Lecturers on this Topic :

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