Acta mathematica scientia,Series A ›› 1999, Vol. 19 ›› Issue (2): 154-158.
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Abstract:
In this paper, one show that finite W-algebras are so-called transverse poisson structure on semisimple Lie algebras.
Key words: W-algebra, Transverse, Poisson structure.')">W-algebra, Transverse, Poisson structure.
CLC Number:
Liu Zhaonan. Finite w-algbras and transverse poisson structure[J].Acta mathematica scientia,Series A, 1999, 19(2): 154-158.
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http://121.43.60.238/sxwlxbA/EN/Y1999/V19/I2/154
１ Ｚａｍｏｌｏｄｃｈｉｋｏｖ Ａ Ｂ．Ｉｎｆｉｎｉｔｅａｄｄｉｔｉｏｎａｌｓｙｍｍｅｔｒｉｅｓｉｎ２ｄｉｍｅｎｓｉｏｎａｌｃｏｎｆｏｒｍａｌｑｕａｎｔｕｍｆｉｅｌｄｔｈｅｏｒｙ．Ｔｈｅｏｒ ＭａｔｈＰｈｙｓ，１９８５，６５，１２０５－１２１３ ２ ＢｏｕｗｋｎｅｇｔＰ，ＳｃｈｏｕｔｅｎｓＫ．ＷＳｙｍｉｎｅｔｒｙｉｎｃｏｎｆｏｒｍａｌｆｉｅｌｄｔｈｅｏｒｙ．ＰｈｙｓＲｅｐ，１９９３，２２３，１８３－２７６ ３ ＦｅｈｅｒＬｅｔａｌ．．ＨａｍｉｌｔｏｎｉａｎｒｅｄｕｃｔｉｏｎｏｆｔｈｅＷｅｓｓＺｕｍｉｎｏＮｏｖｌｏｖＷｉｔｔｅｎｔｈｅｏｒｉｅｓ．ＰｈｙｓＲｅｐ，１９９２，２２２，１－６４ ４ ＪｊｉｎＴ．ＦｉｎｉｔｅＷａｌｇｅｂｒａｓ．ＰｈｙｓＬｅｔｔ，１９９２，Ｂ２９２，６０－６６ ５ Ｔ．ｄｅＢｏｒｅａｎｄＴＪｊｉｎ，ＱｕａｎｔｉｚａｔｉｏｎａｎｄＲｅｐｒｅｓｅｎｔａｔｉｏｎｔｈｅｏｒｙｏｆｆｉｎｉｔｅＷａｌｇｅｂｒａ．ＣｏｍｍｕｎＭａｔｈＰｈｙｓ，１９９３，１５８，４８５－５１６ ６ ＷｅｉｎｓｔｅｉｎＡ．ＴｈｅＬｏｃａｌＳｔｒｕｃｔｕｒｅｏｆＰｏｉｓｓｏｎ Ｍａｎｉｆｏｌｄｓ．ＪＤｉｆｆＧｅｏｍ，１９８３，１８，５２３－５５７ ７ ＯｈＹｏｎｇｇｅｕｎ．ＳｏｍｅＲｅｍａｒｋｓｏｎｔｈｅＴｒａｎｓｖｅｒｓｅＰｏｉｓｓｏｎＳｔｒｕｃｔｕｒｅｓｏｆｃｏａｄｊｏｉｎｔｏｒｂｉｔｓ．ＬｅｔｔＭａｔｈＰｈｙｓ，１９８６，１２，８７－９１ ８ ＶａｉｓｍａＬ．ＬｅｃｔｕｒｅｓｏｎｔｈｅｇｅｏｍｅｔｒｙｏｆＰｏｉｓｓｏｎｍａｎｉｆｏｌｄｓ．ＢｉｒｋｈａｕｓｅｒＶｅｒｌａｇ，１９９４
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