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Socle equivalences of weighted surface algebras
Institution:1. Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100 Toruń, Poland;2. Mathematical Institute, Oxford University, ROQ, Oxford OX2 6GG, United Kingdom;3. Institute of Engineering, Tokyo University of Agriculture and Technology, Nakacho 2-24-16, Koganei, Tokyo 184-8588, Japan;1. Department of Mathematics, University of California, Riverside, Riverside, CA 92521, United States of America;2. Beijing Advanced Innovation Center for Imaging Theory and Technology, Beijing 100048, China;3. Capital Normal University, Academy for Multidisciplinary Studies, Beijing 100048, China;1. Institute of Mathematics of the Czech Academy of Sciences, ?itná 25, 115 67 Prague 1, Czech Republic;2. Laboratory of Algebra and Number Theory, Institute for Information Transmission Problems, Moscow 127051, Russia;3. Charles University, Faculty of Mathematics and Physics, Department of Algebra, Sokolovská 83, 186 75 Praha, Czech Republic;1. Utah State University, Department of Mathematics and Statistics, Logan UT 84341, USA;2. Hung Vuong University, Faculty of Natural Sciences, Viet Tri, Phu Tho, Viet Nam;3. Université Bretagne Sud, Laboratoire de Mathématiques de Bretagne Atlantique, UMR CNRS 6205, Campus de Tohannic, BP 573 F-56017 Vannes, France
Abstract:We describe the structure and properties of the finite-dimensional symmetric algebras over an algebraically closed field K which are socle equivalent to the general weighted surface algebras of triangulated surfaces, investigated in 11]. In particular, we prove that all these algebras are tame periodic algebras of period 4. The main results of this paper form an essential step towards a classification of all symmetric tame periodic algebras of period 4.
Keywords:Syzygy  Periodic algebra  Symmetric algebra  Tame algebra  Surface algebra  Socle equivalence
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