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See detailKrichever-Novikov type algebras. An Introduction
Schlichenmaier, Martin UL

E-print/Working paper (2014)

Krichever--Novikov type algebras are generalizations of the Witt, Virasoro, affine Lie algebras, and their relatives to Riemann surfaces of arbitrary genus. We give the most important results about their ... [more ▼]

Krichever--Novikov type algebras are generalizations of the Witt, Virasoro, affine Lie algebras, and their relatives to Riemann surfaces of arbitrary genus. We give the most important results about their structure, almost-grading and central extensions. This contribution is based on a sequence of introductory lectures delivered by the author at the Southeast Lie Theory Workshop 2012 in Charleston, U.S.A. [less ▲]

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See detailLie superalgebras of Krichever-Novikov type
Schlichenmaier, Martin UL

Scientific Conference (2014, June 29)

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See detailAn elementary proof of the vanishing of the second cohomology of the Witt and Virasoro algebra with values in the adjoint module
Schlichenmaier, Martin UL

in Forum Mathematicum (2014), 26(3), 913-929

By elementary and direct calculations the vanishing of the (algebraic) second Lie algebra cohomology of the Witt and the Virasoro algebra with values in the adjoint module is shown. This yields ... [more ▼]

By elementary and direct calculations the vanishing of the (algebraic) second Lie algebra cohomology of the Witt and the Virasoro algebra with values in the adjoint module is shown. This yields infinitesimal and formal rigidity or these algebras. The first (and up to now only) proof of this important result was given 1989 by Fialowski in an unpublished note. It is based on cumbersome calculations. Compared to the original proof the presented one is quite elegant and considerably simpler. [less ▲]

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See detailSome naturally defined star products for Kaehler manifolds
Schlichenmaier, Martin UL

Scientific Conference (2014, April 02)

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See detailQuasikristalle - 10 zaehlige Symmetrien gibt es nicht - oder doch
Schlichenmaier, Martin UL

Conference given outside the academic context (2014)

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See detailSome naturally defined star products for Kaehler manifolds
Schlichenmaier, Martin UL

Scientific Conference (2014, March 10)

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See detailGeometric Methods in Physics, XXXII Workshop Bialowieza, Poland, Jnue 30 - July 6, 2-13
Schlichenmaier, Martin UL; Kielanowski, Piotr; Bieliavsky, Pierre et al

Book published by Springer (2014)

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See detailMultipoint Lax operator algebras. Almost-graded structure and central extensions
Schlichenmaier, Martin UL

in Sbornik: Mathematics (2014), 205(5), 117-160

Recently, Lax operator algebras appeared as a new class of higher genus current type algebras. Based on I.Krichever's theory of Lax operators on algebraic curves they were introduced by I. Krichever and O ... [more ▼]

Recently, Lax operator algebras appeared as a new class of higher genus current type algebras. Based on I.Krichever's theory of Lax operators on algebraic curves they were introduced by I. Krichever and O. Sheinman. These algebras are almost-graded Lie algebras of currents on Riemann surfaces with marked points (in-points, out-points, and Tyurin points). In a previous joint article of the author with Sheinman the local cocycles and associated almost-graded central extensions are classified in the case of one in-point and one out-point. It was shown that the almost-graded extension is essentially unique. In this article the general case of Lax operator algebras corresponding to several in- and out-points is considered. In a first step it is shown that they are almost-graded. The grading is given by the splitting of the marked points which are non-Tyurin points into in- and out-points. Next, classification results both for local and bounded cocycles are shown. The uniqueness theorem for almost-graded central extensions follows. For this generalization additional techniques are needed which are presented in this article [less ▲]

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See detailFrom the Virasoro Algebra to Krichever–Novikov Type Algebras and Beyond
Schlichenmaier, Martin UL

in Vasil'ev, Alexander (Ed.) Harmonic and Complex Analysis and its Applications (2014)

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See detailKrichever-Novikov type algebras. Theory and Applications
Schlichenmaier, Martin UL

Book published by deGruyter (2014)

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See detailDaniel Sternheimer
Schlichenmaier, Martin UL; Bieliavsky, Pierre

in Goemetric Methods in Physics, XXXII workshop (2014)

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See detailSome naturally defined star products on K\"ahler manifolds
Schlichenmaier, Martin UL

Scientific Conference (2013, October 17)

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See detailSome naturally defined star products on K\"ahler manifolds
Schlichenmaier, Martin UL

Scientific Conference (2013, September 10)

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See detailSome naturally defined star products on K\"ahler manifolds
Schlichenmaier, Martin UL

Scientific Conference (2013, July 02)

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See detailA global operator approach to WZNW models via KN type algebras
Schlichenmaier, Martin UL

Presentation (2013, March 07)

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See detailFrom the Virasoro Algebra to Krichever--Novikov Type Algebras and Beyond
Schlichenmaier, Martin UL

E-print/Working paper (2013)

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See detailGeometric methods in physics. XXXI workshop, Biaowieza, Poland June 24--30, 2012. Selected papers based on the presentations at the workshop.
Kielanowski, Piotr; Ali, Syed Twareque UL; Odesskii, Alexander et al

Book published by Birkhäuser/Springer (2013)

Detailed reference viewed: 54 (6 UL)
See detailGeometric methods in physics. XXX workshop, Bialowieza, Poland June 26 --July 2, 2011. Selected papers based on the presentations at the workshop.
Kielanowski, Piotr; Ali, Syed Twareque UL; Odzijewicz, Anatol et al

Book published by Birkhäuser. (2013)

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See detailLie superalgebras of Krichever-Novikov type and their central extensions
Schlichenmaier, Martin UL

in Analysis and Mathematical Physics (2013), 3(3), 235--261

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See detailAn elementary proof of the formal rigidity of the WItt and Virasoro Algebra
Schlichenmaier, Martin UL

in Kielanowski, Piotr; Ali, Twareque; Odesskii, A;examder (Eds.) et al Geometric Methods in Physics, XXXI Workshop 2012 (2013)

Detailed reference viewed: 115 (6 UL)