$N$-point Virasoro algebras are multi-point Krichever-Novikov type algebras.

Martin Schlichenmaier (U of Luxembourg)

Aug 10. 2022, 10:00 — 11:00

We show how the recently again discussed $N$-point Witt, Virasoro, and affine Lie algebras (partly in relation to representations in field theory) are genus zero examples of the multi-point versions of Krichever--Novikov type algebras as introduced and studied by me some time ago.

Using this more general point of view, useful structural insights and an easier access to calculations can be obtained. The concept of almost-grading will yield information about  triangular decompositions  which are of importance in the theory of representations. 
As examples the algebra of functions, vector fields, differential operators, current algebras, affine Lie algebras, Lie superalgebras
 and their central extensions given.

Very detailed results  for the three-point case are given (if time permits) . 

Further Information
Venue:
ESI Boltzmann Lecture Hall
Recordings:
Recording
Associated Event:
Higher Structures and Field Theory (Thematic Programme)
Organizer(s):
Anton Alekseev (U Genève)
Stefan Fredenhagen (U Vienna)
Nicolai Reshetikhin (UC, Berkeley)
Thomas Strobl (U Lyon)
Chenchang Zhu (U Göttingen)