Introducing Crystalline Graded Algebras

详细信息    查看全文

• 作者：Erna Nauwelaerts (1)
  Freddy Van Oystaeyen (2)
  
• 关键词：Crossed products ; Graded rings ; Weyl algebras ; 16S23 ; 16W50
• 刊名：Algebras and Representation Theory
• 出版年：2008
• 出版时间：April 2008
• 年：2008
• 卷：11
• 期：2
• 页码：133-148
• 全文大小：395KB
• 参考文献：1. Bavula, V.: Generalized Weyl algebras and their representations. Algebrai Analiz. 4(1), (1992) 75鈥?7. English translation in St. Petersburg Math. J. 4(1), 71鈥?2 (1993)
  2. Bavula, V.: Global dimension of generalized Weyl algebras. Conf. Proc. - Can. Math. Soc. 18, 81鈥?07 (1996)
  3. Bavula, V., Van Oystaeyen, F.: Simple holonomic modules over the second Weyl algebra. Adv. Math. 150(1), 80鈥?16 (2000) CrossRef
  4. Bavula, V., Van Oystaeyen, F.: Krull dimension of generalized Weyl algebras and iterated skew polynomial rings. J. Algebra 208(1), 1鈥?4 (1998) CrossRef
  5. Bavula, V., Van Oystaeyen, F.: The simple modules of certain generalized crossed products. J. Algebra 194(2), 521鈥?66 (1997) CrossRef
  6. Jordan, D.A.: Krull and global dimension of certain iterated skew polynomial rings. Contemp. Math. 130, 201鈥?13 (1992)
  7. Huishi, L., Van Oystaeyen, F.: Zariskian Filtrations. Springer (1996)
  8. Jara, P., Lopez, J., Panaite, F., Van Oystaeyen, F.: On iterated twisted tensor products of algebras. (preprint)
  9. Nauwelaerts, E.: Generalized 2-cocycles of finite groups and maximal orders. J. Algebra 210, 225鈥?41 (1998) CrossRef
  10. N膬st膬sescu, C., Van Oystaeyen, F.: Graded Ring Theory, Math. Library vol. 28, North-Holland, Amsterdam (1982)
  11. N膬st膬sescu, C., Van Oystaeyen, F.: Methods of Graded Rings, Lecture Notes in Mathematics. Springer Verlag, Berlin (2003)
  12. Nelis, P., Van Oystaeyen, F.: The projective Schur subgroup of the Brauer group and root groups of finite groups. J. Algebra 137(2), 501鈥?18 (1991) CrossRef
  13. Nauwelaerts, E., Van Oystaeyen, F.: Module characters and projective representations of finite groups. Proc. London Math. Soc. 62(3), 151鈥?66 (1991), 137(2), 501鈥?18 (1991) CrossRef
  14. Nauwelaerts, E., Van Oystaeyen, F.: Finite generalized crossed products over tame and maximal orders. J. Algebra 101, 61鈥?8 (1986) CrossRef
  15. Nauwelaerts, E., Van Oystaeyen, F.: Generalized twisted group rings. J. Algebra 294, 307鈥?20 (2005)
  16. Robson, J.C., Small, L.W.: Liberal extensions. Proc. London Math. Soc. 3, 87鈥?03 (1981) CrossRef
  17. Van Oystaeyen, F.: Azumaya strongly graded rings and ray classes. J. Algebra 103(1), 228鈥?40 (1986), (1, 61鈥?8) CrossRef
  18. Van Oystaeyen, F.: The Algebraic Geometry of Associative Algebras. M. Dekker Monographs, New York (2001)
  
• 作者单位：Erna Nauwelaerts (1)
  Freddy Van Oystaeyen (2)
  
  1. University of Hasselt, Limburg, Belgium
  2. University of Antwerp, Antwerp, Belgium
  
• ISSN：1572-9079

文摘

We develop a generalization of the traditional crossed products and we derive general structural properties. Localization at a particular Ore set is investigated and as a consequence the relation to crossed products is examined. Finally, examples are given.