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Some naturally defined star products for K\"ahler manifolds Schlichenmaier, Martin Scientific Conference (2016, February 18) Detailed reference viewed: 56 (1 UL)Some naturally defined star products for Kaehler manifolds Schlichenmaier, Martin Scientific Conference (2016, January 05) Detailed reference viewed: 49 (2 UL)Berezin-Toeplitz quantization - a lecture course of 5 lectures Schlichenmaier, Martin Presentation (2016, January) Detailed reference viewed: 80 (5 UL)Some naturally defined star products for Kaehler manifolds Schlichenmaier, Martin Scientific Conference (2016) Detailed reference viewed: 51 (0 UL)N-point Virasoro algebras considered as Krichever-Novikov type algebras Schlichenmaier, Martin in Schlichenmaier, Martin; kielianowski, Piotr; Bieliavsky, Piere (Eds.) et al Goemetric Methods in Physics (2016) Detailed reference viewed: 98 (3 UL)Geometric Methods in Physics, Bialowieza 2015 Schlichenmaier, Martin ; ; et al Book published by Birkhaeuser (2016) Detailed reference viewed: 47 (3 UL)Krichever-Novikov type algebras. An introduction Schlichenmaier, Martin in Misra, Kailish; Nakano, Daniel; Parsall, Brian (Eds.) Lie Algebras, Lie Superalgebras, Vertex Algebras and Related Topis (2016) Detailed reference viewed: 69 (4 UL)Krichever-Novikov type algebras and Wess-Zumino-Witten models Schlichenmaier, Martin E-print/Working paper (2015) Krichever--Novikov type algebras are generalizations of the Witt, Virasoro, affine Lie algebras, and their relatives to Riemann surfaces of arbitrary genus and/or the multi-point situation. They play a ... [more ▼] Krichever--Novikov type algebras are generalizations of the Witt, Virasoro, affine Lie algebras, and their relatives to Riemann surfaces of arbitrary genus and/or the multi-point situation. They play a very important role in the context of quantization of Conformal Field Theory. In this review we give the most important results about their structure, almost-grading and central extensions. Furthermore, we explain how they are used in the context of Wess--Zumino--Novikov--Witten models, respectively Knizhnik-Zamolodchikov connections. There they play a role as gauge algebras, as tangent directions to the moduli spaces, and as Sugawara operators. [less ▲] Detailed reference viewed: 80 (1 UL)N point Virasoro algebras considered as Krichever-Novikov type algebras Schlichenmaier, Martin E-print/Working paper (2015) We explain how the recently again discussed $N$-point Witt, Virasoro, and affine Lie algebras are genus zero examples of the multi-point versions of Krichever--Novikov type algebras as introduced and ... [more ▼] We explain how the recently again discussed $N$-point Witt, Virasoro, and affine Lie algebras are genus zero examples of the multi-point versions of Krichever--Novikov type algebras as introduced and studied by Schlichenmaier. Using this more general point of view, useful structural insights and an easier access to calculations can be obtained. As example, explicit expressions for the three-point situation are given. This is a write-up of a talk presented at the Bialowieza meeting in 2015. Details can be found in a recent manuscript by the author. [less ▲] Detailed reference viewed: 122 (1 UL)N point Virasoro Algebras are multi-point Krichever-Novikov type algebras Schlichenmaier, Martin Scientific Conference (2015, October 23) Detailed reference viewed: 107 (4 UL)Some naturally defined star products on Kaehler manifolds Schlichenmaier, Martin Scientific Conference (2015, October 01) Detailed reference viewed: 51 (4 UL)Multi-point Krichever-Novikov type algebras Schlichenmaier, Martin Scientific Conference (2015, July 16) Detailed reference viewed: 56 (4 UL)N-point Virasoro algebras are multi-point Krichever-Novikov type algebras Schlichenmaier, Martin Scientific Conference (2015, June 28) Detailed reference viewed: 112 (0 UL)Some naturally defined star products on Kaehler manifolds Schlichenmaier, Martin Presentation (2015, June 04) Detailed reference viewed: 42 (4 UL)N-point Virasoro algebras are multi-point Krichever--Novikov type algebras Schlichenmaier, Martin E-print/Working paper (2015) We show how the recently again discussed $N$-point Witt, Virasoro, and affine Lie algebras are genus zero examples of the multi-point versions of Krichever--Novikov type algebras as introduced and studied ... [more ▼] We show how the recently again discussed $N$-point Witt, Virasoro, and affine Lie algebras are genus zero examples of the multi-point versions of Krichever--Novikov type algebras as introduced and studied by Schlichenmaier. 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 are studied. Very detailed calculations for the three-point case are given. [less ▲] Detailed reference viewed: 125 (6 UL)Lie Superalgebras of Krichever-Novikov type Schlichenmaier, Martin in KIelanowski, Piotr; Bieliavsky, Pierre; Odzijewicz, Anatol (Eds.) et al Geometric Methods in Physics, Bialowieza XXXIII (2015) Classically, starting from the Witt and Virasoro algebra important examples of Lie superalgebras were constructed. In this write-up of a talk presented at the Bia\l owie\.za meetings we report on results ... [more ▼] Classically, starting from the Witt and Virasoro algebra important examples of Lie superalgebras were constructed. In this write-up of a talk presented at the Bia\l owie\.za meetings we report on results on Lie superalgebras of Krichever-Novikov type. These algebras are multi-point and higher genus equivalents of the classical algebras. he grading in the classical case is replaced by an almost-grading. It is induced by a splitting of the set of points, were poles are allowed, into two disjoint subsets. With respect to a fixed splitting, or equivalently with respect to a fixed almost-grading, it is shown that there is up to rescaling and equivalence a unique non-trivial central extension of the Lie superalgebra of Krichever--Novikov type. It is given explicitly. [less ▲] Detailed reference viewed: 93 (2 UL)Geometric Methods in Physics, XXXIII workshop Bialowieza, Poland Schlichenmaier, Martin ; ; et al Book published by Birkhaeuser (2015) Detailed reference viewed: 48 (2 UL)Lie superalgebras of Krichever-Novikov type Schlichenmaier, Martin Scientific Conference (2014, December 02) Detailed reference viewed: 84 (2 UL)Lie superalgebras of Krichever-Novikov type Schlichenmaier, Martin E-print/Working paper (2014) Classically, starting from the Witt and Virasoro algebra important examples of Lie superalgebras were constructed. In this write-up of a talk presented at the Bia\l owie\.za meetings we report on results ... [more ▼] Classically, starting from the Witt and Virasoro algebra important examples of Lie superalgebras were constructed. In this write-up of a talk presented at the Bia\l owie\.za meetings we report on results on Lie superalgebras of Krichever-Novikov type. These algebras are multi-point and higher genus equivalents of the classical algebras. The grading in the classical case is replaced by an almost-grading. It is induced by a splitting of the set of points, were poles are allowed, into two disjoint subsets. With respect to a fixed splitting, or equivalently with respect to a fixed almost-grading, it is shown that there is up to rescaling and equivalence a unique non-trivial central extension of the Lie superalgebra of Krichever--Novikov type. It is given explicitly. [less ▲] Detailed reference viewed: 105 (2 UL)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) |
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