Skip to main content
×
Home
    • Aa
    • Aa

Homological properties of the enveloping algebra U(Sl2)

  • J. T. Stafford (a1)
Abstract

In this paper we will study the homological properties of the enveloping algebra U = U (Sl2(ℂ)), with particular reference to the homological dimension of simple U-modules and the global dimension of the primitive factor rings of U.

Copyright
References
Hide All
(1)Anderson F. W. and Fuller K. R. Rings and categories of modules (Graduate Texts in Mathematics, no. 13, Springer-Verlag, Berlin, New York, 1974).
(2)Arnal D. and Pinczon G. Idéaux à gauche dans dea quotients simples de l'algèbre enveloppante de sl(2). Bull. Soc. Math. France 101 (1973), 381395.
(3)Bernstein J. N. and Gelfand S. I. Tensor products of finite and infinite dimensional representations of semi-simple Lie algebras. Compositio Math. 41 (1980), 245285.
(4)Bhatwadekar S. On the global dimension of some filtered algebras. J. London Math. Soc. 13 (1976), 239248.
(5)Borho W. and Rentschler R. Oresche Teilmengen in Einhullenden Algebren. Math. Ann. 217 (1975), 201210.
(6)Cartan H. and Eilenberg S. Homological algebra (Princeton University Press, Princeton, 1956).
(7)Dixmier J. Enveloping algebras (North Holland, Amsterdam, 1977).
(8)Dixmier J. Quotients simple de l'algèbre enveloppante de sl 2. J. Algebra. 24 (1973), 551564.
(9)Fields K. L. On the global dimension of skew polynomial rings – an addendum. J. Algebra 14 (1970), 528530.
(10)Rentschler R. and Gabriel P. Sur la dimension dea anneaux et ensembles ordonnés. C.R. Acad. Sci. Paris (A) 265 (1967), 712715.
(11)Roos J.-E. Compléments a l'étude des quotients primitifs des algèbres enveloppantes des algèbres de Lie semi-simples. C.R. Acad. Sci. Paris (A), 276 (1973), 447450.
(12)Rotman J. J. An introduction to homological algebra (Academic Press, London, 1979).
(13)Smith S. P. The primitive factor rings of the enveloping algebra of sl(2, C) Proc. London Math. Soc. 24 (1981), 97108.
(14)Stafford J. T. Completely faithful modules and ideals of simple Noetherian rings. Bull. London Math. Soc. 8 (1976), 168173.
(15)Stafford J. T. Stable structure of noncommutative Noetherian rings. J. Algebra. 47 (1977), 244267.
(16)Stafford J. T. Generating modules efficiently: Algebraic K-theory for noncommutative Noetherian rings. J. Algebra 69 (1981), 312346.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 7 *
Loading metrics...

Abstract views

Total abstract views: 54 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 21st October 2017. This data will be updated every 24 hours.