PhD in Pure and Applied Mathematics

Una introduzione alle algebre di Hopf (Corso Dottorato)

An Introduction to Hopf Algebras (Ph.D. Course)

Academic year 2014/2015

Sommario del corso

• Course objectives
• Learning assessment methods
• Program
• Suggested textbooks and readings
• Notes
• Teaching tools

Course objectives

The course is intended to give an introduction to the basic notions and some of the main results related to Hopf algebra Theory from an algebraic point of view.

Learning assessment methods

Ita: Da concordarsi con il docente. Eng: To be arranged with the lecturer.

Program

We plan to focus on some of the following topics depending both on the time and on the interest of the audience.

-          Coalgebras, Bialgebras and Hopf algebras and their properties

-          Examples: Group algebra, Tensor algebra, Symmetric algebra, Universal Enveloping algebras of a Lie algebra, Taft Algebra.

-          The dual of a Hopf algebra.

-          Comodules, Hopf modules. Fundamental Theorem of Hopf modules, integrals.

-          Hopf algebras with a projection and Bosonizations.

-          Overview of the elements of Category theory: Categories, Functors, Yoneda Lemma. Commutative Hopf algebras and affine group schemes.

- H.-J. Schneider, Lectures on Hopf algebras, notes by S. Natale. (www.famaf.unc.edu.ar/andrus/papers/Schn1.pdf)

- M. E. Sweedler,  Hopf algebras. Mathematics Lecture Note Series W. A. Benjamin, Inc., New York 1969.

- E. Abe, Hopf algebras. Translated from the Japanese by Hisae Kinoshita and Hiroko Tanaka. Cambridge Tracts in Mathematics, 74. Cambridge University Press, Cambridge-New York, 1980.

- S. Montgomery, Hopf algebras and their actions on rings. CBMS Regional Conference Series in Mathematics, 82. Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 1993.

- C. Kassel, Quantum groups. Graduate Texts in Mathematics, 155. Springer-Verlag, New York, 1995.

- S. Majid, Foundations of quantum group theory. Cambridge University Press, Cambridge, 1995.

- S. Dăscălescu, C. Năstăsescu, S. Raianu, Hopf algebras. An introduction. Monographs and Textbooks in Pure and Applied Mathematics, 235. Marcel Dekker, Inc., New York, 2001.

- D. E. Radford, Hopf algebras. Series on Knots and Everything, 49. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2012.

Note

The course will be held in English on demand.

• Teaching materials
• Exams and finals
• Go to Moodle
• Visit the forums