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On quantum toroidal algebra of type A1
Authors:Fulin Chen  Naihuan Jing  Fei Kong  Shaobin Tan
Affiliation:1. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, China;2. Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA;3. Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education), School of Mathematics and Statistics, Hunan Normal University, Changsha, 410081, China;1. Tata Institute of Fundamental Research, School of Mathematics, Mumbai, India;2. Osnabrück University, Institute of Mathematics, Osnabrück, Germany;1. School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai-40005, India;2. Organization for the Strategic Coordination of Research and Intellectual Properties, Meiji University, Japan;3. Department of Mathematics, College of Humanities and Sciences, Nihon University, Setagaya-Ku, Tokyo 156-0045, Japan;1. Institute of Mathematics for Industry, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan;2. Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Givat Ram, Jerusalem 9190401, Israel;3. Max Planck Institute for Mathematics in the Sciences, Inselstr. 22, 04103 Leipzig, Germany
Abstract:In this paper we introduce a new quantum algebra which specializes to the 2-toroidal Lie algebra of type A1. We prove that this quantum toroidal algebra has a natural triangular decomposition, a (topological) Hopf algebra structure and a vertex operator realization.
Keywords:Quantum toroidal algebra  Triangular decomposition  Hopf algebra
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