COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring. |

University of Cambridge > Talks.cam > Algebra and Representation Theory Seminar > Coloured Kac-Moody algebras

## Coloured Kac-Moody algebrasAdd to your list(s) Download to your calendar using vCal - Alexandre Bouayad (University of Cambridge)
- Wednesday 05 November 2014, 16:30-17:30
- MR12.
If you have a question about this talk, please contact David Stewart. I will present a new approach to deformations of a Kac-Moody algebra g (of it universal enveloping algebra U(g) more precisely) and of its modules. The construction is meant to be both elementary and systematic. We will start with the easiest case, that is to say with the Lie algebra sl2, by colouring the crystal graphs of the Verma modules of sl2 with deformations of the natural numbers. We will explain how a given colouring defines a deformation of the Verma modules of sl2. We will see how deformed Verma modules of sl2 can generate a deformation of the rigid monoidal category mod(g) of g-modules. Colourings provide in fact a classification of the deformations of the category mod(g). By Tannaka duality, we will then obtain that colourings form a groupoid, isomorphic to the groupoid of deformations of the Hopf algebra U(g). We will retrieve in particular the Drinfeld-Jimbo quantum algebra from a colouring by q-numbers. Coloured Kac-Moody algebras were originally devised by the speaker to solve conjectures of Frenkel-Hernandez, related to the Langlands duality for quantum groups. We will see that two isogenic coloured Kac-Moody algebras can be interpolated by a third coloured Kac-Moody algebra, implying in particular a solution to the conjectures. We will also discuss the existence of a potential link between coloured Kac-Moody algebras and quiver Hecke algebras of Khovanov-Lauda-Rouquier. This may pave the way to a categorification and to a geometric realisation of coloured Kac-Moody algebras, with eventual connections to the geometric Langlands correspondence. We will lastly evoke other possible applications of coloured Kac-Moody algebras This talk is part of the Algebra and Representation Theory Seminar series. ## This talk is included in these lists:- Algebra and Representation Theory Seminar
- All CMS events
- All Talks (aka the CURE list)
- CMS Events
- DPMMS Lists
- DPMMS Pure Maths Seminar
- DPMMS info aggregator
- DPMMS lists
- Hanchen DaDaDash
- Interested Talks
- MR12
- School of Physical Sciences
- bld31
Note that ex-directory lists are not shown. |
## Other listsTransition Cambridge Perspectives on Inclusive and Special Education DAMTP BioLunch## Other talksPruning and grafting syntactic trees for cross-lingual transfer tasks The world is not flat: towards 3D cell biology and 3D devices Small Opuntioideae Simulating Electricity Prices: negative prices and auto-correlation Cambridge-Lausanne Workshop 2018 - Day 1 |