Die multiplikative Verknüpfung in den Verlinde Algebren über SU(2)

Reisert, Pascal (29. April 2009): Die multiplikative Verknüpfung in den Verlinde Algebren über SU(2). Bachelor, Faculty of Mathematics, Computer Science and Statistics, Ludwig-Maximilians-Universität München.

Abstract

In der vorliegenden Bachelorarbeit entwickeln wir die multiplikative Struktur der Verlinde Algebren über dem Darstellungsring von SU(2) mit Methoden der Darstellungstheorie.

• Item Type: LMU Munich: Thesis
• Keywords: Darstellungstheorie von Lie-Gruppen; Verlinde Algebra; SU(2)
• Faculties: Mathematics, Computer Science and Statistics > Mathematics
• Institut or Department: Mathematisches Institut
• Subjects: 500 Science > 510 Mathematics
• Language: German

References

[1] Frank W. Anderson and Kent R. Fuller, Rings and Categories of Module, Springer, New York, 1992.

[2] Asim O. Barut and Ryszard Raczka, Theory of Group Reprensentations and Applications, Polish Scientific Publishers, Warszawa, 1977.

[3] Siegfried Bosch, Algebra, Springer, Berlin, 2006.

[4] Raoul Bott, On E. Verlinde's Formula in the Context of Stable Bundles, Trieste Conference on Topological Methods in Quantum Field Theories (1991), 84-95.

[5] Theodor Bröcker and Tamma tom Dieck, Representations of compact Lie Groups, Springer, Berlin, 2003.

[6] Ilja N. Bronstein, Konstantin A. Semendjajew, Gerhard Musiol, Heiner Mühlig, Taschenbuch der Mathematik, Harry Deutsch, Frankfurt am Main, 2001.

[7] Gerd Faltings, A proof of Verlinde formula, Journal for Algebraic Geometry 3 (1994), 347- 374.

[8] Gerd Faltings, Thetafunktionen auf Modulräumen von Vektorbündeln, Jahresbericht der DMV 110 (2008), 3-18.

[9] Daniel Freed, The Verlinde algebra is twisted equivariant K-theory, Turkish J. Math. 25 (2001), 159-167.

[10] Daniel Freed, Michael Hopkins, Constantin Teleman, Loop Groups and twisted K-theory III 26 (2013), 595-644.

[11] Edwin Hewitt and Kenneth A. Ross, Abstract Harmonic Analysis I, Springer, Berlin, 1994.

[12] Joachim Hilgert and Karl-Hermann Neeb, Lie-Gruppen und Lie-Algebren, Vieweg, 1991.

[13] D. Husemöller, M. Joachim, B. Jurco, M. Schottenloher, Basic Bundle Theory and K-Cohomology Invariants, Springer, Berlin, 2008.

[14] Gordon James and Martin Liebeck, Representations and Characters of Groups, Cambridge University Press, 2001.

[15] Klaus Jänich, Topology, Springer, Berlin, 2005.

[16] Jürgen Jost, Riemannian Geometry and Geometric Analysis, Springer, Berlin, 2008.

[17] Micheal Reed and Barry Simon, Methods of Modern Mathematical Physics, Vol. 1: Functional Analysis, Academic Press, INC., London, 1980.

[18] Martin Schottenloher, Geometrie und Symmetrie in der Physik, Vieweg Verlagsgesellschaft, 1995.

[19] Martin Schottenloher, A Mathematical Introduction to Conformal Field Theory, Springer, Berlin, 2008.

[20] Mitsuo Sugiura, Unitary Representations and Harmonic Analysis: An Introduction (North- Holland Mathematical Library), Elsevier Science Publishing Co Inc., U.S. Auflage, 1990.

[21] Andras Szenes, The combinatorics of the Verlinde formula, Cambridge University Press, Cambridge, 1995.

[22] Constantin Teleman, K-theory of the moduli of principal bundles on a surface and deformations of the Verlinde algebra, Topology, Geometry and Quantum Field Theory: Proceedings of the 2002 Oxford Symposium in Honour of the 60th Birthday of Graeme Segal, CUP, 2004.

[23] Erik Verlinde, Fusion rules and modular transformations in two-dimensional conformal field theory, Nuclear Physics B 300 (1988), 360-376.