N-Point Virasoro Algebras are multipoint Krichever-Novikov type algebras

Presentation (2022, August 10)

Krichever-Novikov type algebras. A general review and the Genus Zero case

in Hervig, Sigbjorn; Kruglikov, Boris; Markina, Irina (Eds.) et al Geometry, Lie theory and applications (2022)

The low-dimensional algebraic cohomology of the Witt and the Virasoro algebra with values in natural modules

in Banach Center Publications (2021), 123

The main aim of this contribution is to compute the low-dimensional algebraic cohomology of the Witt and the Virasoro algebra with values in the adjoint and the trivial module. The last section includes ... [more ▼]

The main aim of this contribution is to compute the low-dimensional algebraic cohomology of the Witt and the Virasoro algebra with values in the adjoint and the trivial module. The last section includes results for the general tensor densities modules, presented without proof. One of our main results is that the third algebraic cohomology of the Witt algebra with values in the adjoint module vanishes, while it is one-dimensional for the Virasoro algebra. The first and the second algebraic cohomology of the Witt and the Virasoro algebra with values in tensor densities modules vanish for almost all modules. In the case they do not vanish, we give explicit expressions for the generating cocycles. In our work, we consider algebraic cohomology and not only the sub-complex of continuous cohomology, meaning we do not put any continuity constraints on the cochains. Consequently, our results are independent of any choice of an underlying topology, and valid for any concrete realizations of the considered Lie algebras. [less ▲]

Berezin-Toeplitz quantization - an overview

Presentation (2020, March 13)

Some naturally defined star products for Kaehler manifolds

Scientific Conference (2019, September 10)

Canonical quantization for compact quantizable Kaehler manifolds

Scientific Conference (2019, May 02)

Krichever-Novivkov type algebras. A general review and the genus zero case

E-print/Working paper (2019)

In the first part of this survey we recall the definition and some of the constructions related to Krichever--Novikov type algebras. Krichever and Novikov introduced them for higher genus Riemann surfaces ... [more ▼]

In the first part of this survey we recall the definition and some of the constructions related to Krichever--Novikov type algebras. Krichever and Novikov introduced them for higher genus Riemann surfaces with two marked points in generalization of the classical algebras of Conformal Field Theory. Schlichenmaier extended the theory to the multi-point situation and even to a larger class of algebras. The almost-gradedness of the algebras and the classification of almost-graded central extensions play an important role in the theory and in applications. In the second part we specialize the construction to the genus zero multi-point case. This yields beside instructive examples also additional results. In particular, we construct universal central extensions for the involved algebras, which are vector field algebras, differential operator algebras, current algebras and Lie superalgebras. We point out that the recently (re-)discussed $N$-Virasoro algebras are nothing else as multi-point genus zero Krichever-Novikov type algebras. The survey closes with structure equations and central extensions for the three-point case. [less ▲]

Krichever-Novikov Type Algebras and Wess-Zumino-Novikov-Witten Models

in Uniformization, Riemann-Hilbert Correspondence, Calabi-Yau Manifolds, and Picard-Fuchs Equations (2018)

Krichever-Novikov type algebras. Definitions and Results

E-print/Working paper (2018)

ICAMI 2017: International Conference on Applied Mathematics and Informatics: Forum on Analysis, Geometry, and Mathematical Physics

in Analysis and Mathematical Physics (2018), 8