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Atlantic Association for Research in the Mathematical Sciences
Atlantic Algebra Centre  

Nichols Algebras

Mini course by

Professor István Heckenberger

University of Marburg, Germany
March 14 - 18, 2016

 

Nichols algebras are natural braided Hopf algebras appearing in the structure theory of quantum groups and pointed Hopf algebras and in non-commutative differential geometry. The most trivial examples are polynomial rings and exterior algebras. Albeit it is not clear from the various equivalent definitions, there are many deep relationships of Nichols algebras to other fields of mathematics, in particular to Coxeter groups and Lie theory. The aim of the mini course is to introduce the fundamental concepts of the theory and to work out the intrinsic combinatorics in some typical cases. If possible, an outlook to more general settings will be given.

Professor Heckenberger is one of the world-leading experts in the field. His introduction of arithmetic root systems and Weyl groupoids into the theory constituted a turning point of the development. The lectures will be accessible to graduate and advanced undergraduate students. In addition to the mini course, he will give a colloquium talk on Fomin-Kirillov algebras at the Department of Mathematics and Statistics at ÐÓ°É´«Ã½ University that is aimed at a more general mathematical audience.

The schedule of the mini course is

Monday, March 14, 12:00 m - 1:30 pm, SN 2101
Tuesday, March 15, 2:30 pm - 3:45 pm, SN 2098
Wednesday, March 16, 12:00 m - 1:50 pm, SN 2105
Thursday, March 17, 12:00 m - 12:50 pm, SN 2041 
Thursday, March 17, 2:30 pm - 3:45 pm, SN 2098
Friday, March 18, 3:00 pm - 3:50 pm, SN 2098