Krichever-Novikov algebras are infinite-dimensional Lie algebras which generalise the Witt algebra and loop algebras. They have many connections with mathematical physics. This is the website for the reading seminar on them, which runs at the University of Edinburgh from September-December 2021. For the Zoom link, contact Sue Sierra.
We will post videos of any talks given online.
Tentative schedule of talks and topics:
Introductory lecture (Sue Sierra, 1 October) slides
Explicit basis and generators (Rekha Biswal, 22 October) video
Central extensions (Jose Figueroa-O'Farrill, 29 October) video slides
Verma modules and fermionic representations (Johan Martens, 5 November) video slides
NO SEMINAR 12 November
Fermionic representations (Sue Sierra, 19 November) video slides
Sugawara construction (Rekha Biswal, 26 November) video
KN-algebras and global deformations of the Virasoro algebra (Lucas Buzaglo, 10 December) video slides
Potentially next semester we will have a followup lecture or two where we talk about WZNW-models or relations between KN-algebras and W-algebras, but those aren't scheduled for now.
References
References for the seminar include:
Krichever-Novikov Type Algebras: Theory and Applications, by Schlichenmaier. Contact Sue Sierra for access.
The survey article From the Virasoro algebra to Krichever-Novikov type algebras and beyond, by Schlichenmaier.
Affine Krichever-Novikov algebras, their representations, and applications, by Sheinman, which focuses on affine and current algebras of KN type.
Global deformations of the Witt algebra of KN type, by Fialovski and Schlichenmaier.