hopf algebras

san francisco state university

universidad de los andes

federico ardila

2012

. hopf cafe . homework . lectures . people . projects . syllabus . texts .

The following is a list of books and other resources that you might find helpful. I have some of these in my office, in case you want to borrow them.

I will not follow a particular textbook. Our main sources for the course are:

o M. Aguiar and S. Mahajan. Monoidal functors, species, and Hopf algebras.

o S. Montgomery. Hopf algebras and their actions on rings.

o M. Sweedler. Hopf algebras

A great way to learn about recent developments and find open problems is to visit the math arXiv, where many researchers post their papers before they are officially published (and keep them there afterwards). You can search for any keywords that interest you.

A (necessarily incomplete) list of related books:

o E. Abe. Hopf algebras

o M. Aguiar and S. Mahajan. Coxeter groups and Hopf algebras.

o A. Balachandran, S. Jo, G. Marmo. Group theory and Hopf algebras: lectures for physicists.

o S. Chase and M. Sweedler. Hopf algebras and Galois theory.

o A. Zelevinsky. Representations of finite classical groups. A Hopf algebra approach.

An even more incomplete list of interesting papers:

Some recent combinatorial papers.

o M. Aguiar. Structure of the Malvenuto-Reutenauer Hopf algebra of permutations

o M. Aguiar and F. Ardila. The Hopf monoid of generalized permutahedra.

o M. Aguiar, N. Bergeron, and F. Sottile. Combinatorial Hopf algebras and generalized Dehn-Sommerville relations.

o AIM paper (28 authors). Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras.

o N. Bergeron and M. Zabrocki. The Hopf algebras of symmetric functions and quasisymmetric functions in non-commutative variables are free and cofree

o R. Ehrenborg. On posets and Hopf algebras.

o F. Fisher. CoZinbiel Hopf algebras in combinatorics.

o S. Forcey, A. Lauve, and F. Sottile. New Hopf structures on binary trees.

o F. Hivert, J.-C. Novelli and J.-Y. Thibon. Commutative combinatorial Hopf algebras.

o A. Lauve, T. Lam, F. Sottile. Skew Littlewood-Richardson rules from Hopf Algebras.

o J.-L. Loday and M. Ronco. Combinatorial Hopf algebras.

o J.-L. Loday and M. Ronco. Hopf algebra of the planar binary trees.

o C. Malvenuto and C. Reutenauer. Duality between quasi-symmetric functions and the Solomon descent algebra.

o N. Reading. Lattice congruences, fans and Hopf algebras

o W. Schmitt. Incidence Hopf algebras.

Some "classic" and survey papers on Hopf algebras.

o N. Andruskiewitsch. About finite dimensional Hopf algebras.

o P. Cartier. A primer on Hopf algebras.

o H. Cohn. Quantum groups.

o V. Drinfeld. Hopf algebras and the quantum Yang-Baxter equation.

o G. Duchamp, P. Blasiak, A. Horzela, K. Penson, A. Solomon. Hopf algebras in general and in combinatorial physics: a practical introduction.

o S. Joni and G.-C. Rota. Coalgebras and bialgebras in combinatorics.

o J. Milnor and J. Moore. On the structure of Hopf algebras.

o D. Radford. The order of the antipode of a finite dimensional Hopf algebra is finite.

o Y. Sommerhauser. On Kaplansky's conjectures.

o E. Taft. The order of the antipode of finite-dimensional Hopf algebra.