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Lecture Topic : (Pure Math) QUANTUM  GROUPS (M2, Kassel)

Prerequisites : Finite Group Theory (Sen, M1); Category Theory (M2); Representation Theory (M1); Knot Theory (M1); Lie Algebras (M1); Quantum Groups (M1,2); Homology and Cohomology (M2); Braid Groups (M2);

Recommended Text(s) :

“Quantum Groups”, Christian Kassel, Gradate Texts in Mathematics 155, Springer, 1995

Approx price new on (hard copy) : $76

Approx price second hand on (hard copy) : $53

Availability free on (e-format) : Yes

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

Lectures and Links :

Lecture 1  (link)

Ch.1   Preliminaries

Ch.2   Tensor Products

Lecture 2  (link)

Ch.3   The Language of Hopf Algebras

Ch.4   The Quantum Plane and Its Symmetries

Lecture 3  (link)

Ch.5   The Lie Algebra of SL(2)

Ch.6   The Quantum Enveloping Algebra of sl(2)

Lecture 4  (link)

Ch.7  A Hopf Algebra Structure on Uq(sl(2))

Ch.8   The Yang-Baxter Equation and (Co) Braided Bialgebras

Lecture 5  (link)

Ch.9   Drinfeld’s Quantum Double

Ch.10   Knots, Links, Tangles, and Braids

Lecture 6  (link)

Ch.11   Tensor Categories

Ch.12   The Tangle Category

Lecture 7  (link)

Ch.13   Braidings

Ch.14   Dualities in Tensor Categories

Lecture 8  (link)

Ch.15   Quasi Bialgebras

Ch.16   Generalities on Quantum Enveloping Algebras

Lecture 9  (link)

Ch.17   Drinfeld and Jimbo’s Quantum Enveloping Algebras

Ch.18   Cohomology and Rigidity Theorems

Lecture 10  (link)

Ch.19   Monodromy of the Knizhnik-Zamolodchikov Equations

Ch.20   Postlude : A Universal Knot Invariant

Links to Other Lecturers on this Topic :

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