1. 'Classical' Flag Varieties for Quantum Groups: The Standard Quantum SL(n,C)
- Author
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Christian Ohn, Laboratoire de Mathématiques de Reims (LMR), Université de Reims Champagne-Ardenne (URCA)-Centre National de la Recherche Scientifique (CNRS), and Arxiv, Import
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Pure mathematics ,Mathematics(all) ,General Mathematics ,Carry (arithmetic) ,Secondary 14M15, 16S38, 17B37 ,01 natural sciences ,Primary 20G42 ,Mathematics - Algebraic Geometry ,Simple (abstract algebra) ,Mathematics::K-Theory and Homology ,Mathematics::Quantum Algebra ,0103 physical sciences ,Mathematics - Quantum Algebra ,[MATH.MATH-RA] Mathematics [math]/Rings and Algebras [math.RA] ,FOS: Mathematics ,Quantum Algebra (math.QA) ,0101 mathematics ,Quantum ,Algebraic Geometry (math.AG) ,Mathematics ,[MATH.MATH-QA] Mathematics [math]/Quantum Algebra [math.QA] ,Quantum group ,010102 general mathematics ,[MATH.MATH-RA]Mathematics [math]/Rings and Algebras [math.RA] ,Mathematics::Rings and Algebras ,[MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG] ,Mathematics - Rings and Algebras ,Noncommutative geometry ,Algebra ,Rings and Algebras (math.RA) ,[MATH.MATH-QA]Mathematics [math]/Quantum Algebra [math.QA] ,010307 mathematical physics ,[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG] ,Variety (universal algebra) ,Flag (geometry) - Abstract
We suggest a possible programme to associate geometric "flag-like" data to an arbitrary simple quantum group, in the spirit of the noncommutative algebraic geometry developed by Artin, Tate, and Van den Bergh. We then carry out this programme for the standard quantum SL(n) of Drinfel'd and Jimbo, where the varieties involved are certain T-stable subvarieties of the (ordinary) flag variety., 27 pages; needs LaTeX2e, AMS-LaTeX, XY-pic, and PSTricks (v2: several minor corrections)
- Published
- 2002
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