Construction of classical Virasoro algebras as SU(1,1) extensions |
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| Institution: | 1. Department of Mathematical Sciences, University of Durham, Durham DH1 3LE, UK;2. Departement de Physique, Université de l''État à Mons, 19 Avenue Maistriau, B-7000 Mons, Belgium;1. Institute of Mathematics, University of Tsukuba, 1-1-1 Tennodai Tsukuba, Ibaraki, 305-8571, Japan;2. University ‘Al. I. Cuza’ of Iasi, Faculty of Mathematics, Bd. Carol I, no. 11, 700506 Iasi, Romania;1. Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul 08826, Republic of Korea;2. Department of Mathematical Sciences, Seoul National University, Seoul 08826, Republic of Korea;1. Department of Mathematics, University of Cádiz, Spain;2. Department of Mathematics and Applied Mathematics, University of Cape Town, South Africa;1. Universite de Tunis El Manar, Faculte des sciences de Tunis, Unite des Nanomateriaux et Photonique, 2092, El Manar, Tunisia;2. Laboratoire Charles Coulomb – UMR 5221 CNRS, University of Montpellier, Place Bataillon, 34095, Montpellier, France;1. Department of Mathematics and Statistics, Lancaster University, Lancaster, LA1 4YF, United Kingdom;2. Institut für Algebra, Zahlentheorie und Diskrete Mathematik, Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, Germany;1. Faculty of Mathematics, National Research University HSE, Russian Federation;2. St. Petersburg Department of Steklov Institute of Mathematics, St. Petersburg State University, Russian Federation |
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| Abstract: | The generators of SU(1,1) and their Casimir invariant may be arrayed in a compact formula to construct all generators of the centreless Virasoro algebra which includes this SU(1,1) subalgebra. We illustrate properties of our construction through a simple differential operator realization of these algebras and comment on its usefulness. |
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