Child pages
  • Introduction to Hopf algebras and representations, spring 2011

Versions Compared

Key

  • This line was added.
  • This line was removed.
  • Formatting was changed.

...

Algebra I and a good command of linear algebra

Lectures

A set The current version of the lecture notes consisting essentially of corrected is: Hopf_algebras_and_representations.pdf. This essentially consist of corrected and slightly reorganized versions of the sketches below is in preparation. Comments and remarks about misprints are welcome!

...

Sketches of lecture notes

The current version of the lecture notes of the entire course is here: Hopf_algebras_and_representations.pdf

Older versions are still attached to the following schedule of lectures.

  • 18.1.2011: Jordan canonical form (lecture_sketch-Jordan_normal_form.pdf), Representations of finite groups part 1 (contained in the file below)
  • 25.1.2011: Representations of finite groups part 2 (contained in the file below), Tensor products of vector spaces (contained in the file below)
  • 1.2.2011: Representations of finite groups part 3 (lecture_sketch-representations_of_finite_groups.pdf), Algebras (contained in the file below)
  • 8.2.2011: Algebras & coalgebras & bialgebras & Hopf algebras (contained in the file below), Some more remarks about tensor products (lecture_sketch-tensor_products.pdf)
  • 15.2.2011: Algebras etc. & convolution products & properties of the antipode (contained in the file below)
  • 22.2.2011: Algebras etc. & representations & restricted dual (contained in the file below)
  • 1.3.2011: Algebras etc. & restricted duals (lecture_sketch-algebras_coalgebras_etc.pdf), On quantum groups: restricted dual of the building block (contained in the file below)
  • 15.3.2011: On quantum groups: Yang-Baxter equation and braided bialgebras (contained in the file below)
  • 22.3.2011: On quantum groups: the Drinfeld double construction (contained in the file below)
  • 29.3.2011: On quantum groups: U_q(sl_2) and the Drinfeld double of the building block (contained in the file below)
  • 5.4.2011: On quantum groups: representations of U_q(sl_2), semisimplicity (contained in the file below)
  • 12.4.2011: On quantum groups: semisimplicity of U_q(sl_2) for q not a root of unity, infinite dimensional Drinfeld doubles and Yang-Baxter equation (lecture_sketch-on_quantum_groups.pdf)
  • 19.4.2011: Discussion of knots, links and tangles and graphical calculus in finite dimensional modules over braided Hopf algebras
  • 3.5.2011: Discussion of graphical calculus in finite dimensional modules over ribbon Hopf algebras and invariants of knots, links and tangles