Nichols Algebras and Their Interactions with Lie Theory, Hopf Algebras and Tensor Categories (15w5053)


(Universidad Nacional de Cordoba)


(University of Marburg)

(University of Washington)

Sarah Witherspoon (Texas A&M University)

(University of Washington)


The Banff International Research Station will host the "Nichols Algebras and Their Interactions with Lie Theory, Hopf Algebras and Tensor Categories" workshop from September 6th to September 11th, 2015.

Today's mathematics is much more than just the study of numbers, equations, functions, and probabilities.
The notion of an algebra is a far reaching generalization of a system of equations, and algebras are used
to describe geometrical objects, physical phenomena, data encoding, and many other things. Some algebras
have a simple structure, some of them are very complicated. It is often very important to understand the
internal symmetry of an algebra to be able to analyze effectively its structure and to develop
applications. A rich symmetry and the appearance in different mathematical contexts is usually a good
indication for an interesting algebra.

The topic of the proposed workshop is {it Nichols algebras} which do exhibit beautiful symmetries and
appear in a wide array of mathematical and physical applications. They were first studied by Nichols in
1978 on the way of classifying certain Hopf algebras, another long-studied class of algebras which appear
in algebra, geometry, topology, and physics. In the late 80's Nichols algebras were rediscovered by
Woronowicz and Lusztig in the contexts of non-commutative differential calculus and quantum groups,
respectively. Even more recently it was discovered that Nichols algebras appear naturally in logarithmic
conformal field theories. Because of the many open fundamental questions on Nichols algebras and their
applications, their study remains an interesting and important challenge for the future.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).