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Krichever-Novikov type algebras. An Introduction Schlichenmaier, Martin 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 ▲] Detailed reference viewed: 70 (3 UL)Lie superalgebras of Krichever-Novikov type Schlichenmaier, Martin Scientific Conference (2014, June 29) Detailed reference viewed: 91 (4 UL)An elementary proof of the vanishing of the second cohomology of the Witt and Virasoro algebra with values in the adjoint module Schlichenmaier, Martin 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 The first (and up to now only) proof of this important result was given 1989 by Fialowski in an unpublished note.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 ▲] Detailed reference viewed: 158 (14 UL)Some naturally defined star products for Kaehler manifolds Schlichenmaier, Martin Scientific Conference (2014, April 02) Detailed reference viewed: 44 (2 UL)Quasikristalle - 10 zaehlige Symmetrien gibt es nicht - oder doch Schlichenmaier, Martin Conference given outside the academic context (2014) Detailed reference viewed: 69 (4 UL)Some naturally defined star products for Kaehler manifolds Schlichenmaier, Martin Scientific Conference (2014, March 10) Detailed reference viewed: 41 (4 UL)Geometric Methods in Physics, XXXII Workshop Bialowieza, Poland, Jnue 30 - July 6, 2-13 Schlichenmaier, Martin ; ; et al Book published by Springer (2014) Detailed reference viewed: 58 (3 UL)Multipoint Lax operator algebras. Almost-graded structure and central extensions Schlichenmaier, Martin 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 ▲] Detailed reference viewed: 198 (5 UL)From the Virasoro Algebra to Krichever–Novikov Type Algebras and Beyond Schlichenmaier, Martin in Vasil'ev, Alexander (Ed.) Harmonic and Complex Analysis and its Applications (2014) Detailed reference viewed: 172 (6 UL)Krichever-Novikov type algebras. Theory and Applications Schlichenmaier, Martin Book published by deGruyter (2014) Detailed reference viewed: 76 (3 UL)Daniel Sternheimer Schlichenmaier, Martin ; in Goemetric Methods in Physics, XXXII workshop (2014) Detailed reference viewed: 99 (3 UL)Some naturally defined star products on K\"ahler manifolds Schlichenmaier, Martin Scientific Conference (2013, October 17) Detailed reference viewed: 71 (7 UL)Some naturally defined star products on K\"ahler manifolds Schlichenmaier, Martin Scientific Conference (2013, September 10) Detailed reference viewed: 50 (4 UL)Some naturally defined star products on K\"ahler manifolds Schlichenmaier, Martin Scientific Conference (2013, July 02) Detailed reference viewed: 53 (2 UL)A global operator approach to WZNW models via KN type algebras Schlichenmaier, Martin Presentation (2013, March 07) Detailed reference viewed: 59 (3 UL)From the Virasoro Algebra to Krichever--Novikov Type Algebras and Beyond Schlichenmaier, Martin E-print/Working paper (2013) Detailed reference viewed: 114 (2 UL)Geometric methods in physics. XXXI workshop, Biaowieza, Poland June 24--30, 2012. Selected papers based on the presentations at the workshop. ; Ali, Syed Twareque ; et al Book published by Birkhäuser/Springer (2013) Detailed reference viewed: 54 (6 UL)Geometric methods in physics. XXX workshop, Bialowieza, Poland June 26 --July 2, 2011. Selected papers based on the presentations at the workshop. ; Ali, Syed Twareque ; et al Book published by Birkhäuser. (2013) Detailed reference viewed: 80 (6 UL)Lie superalgebras of Krichever-Novikov type and their central extensions Schlichenmaier, Martin in Analysis and Mathematical Physics (2013), 3(3), 235--261 Detailed reference viewed: 172 (6 UL)An elementary proof of the formal rigidity of the WItt and Virasoro Algebra Schlichenmaier, Martin 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) |
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