Extensions of modules over Weyl algebras
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Abstract:
In this paper we calculate some $\mathrm {Ext}$ groups of singular modules over the complex Weyl algebra $A_{n}$. In particular we determine conditions under which $\mathrm {Ext}$ is an infinite dimensional vector space when $n =2$ or $3$.References
- Joseph Bernstein and Valery Lunts, On nonholonomic irreducible $D$-modules, Invent. Math. 94 (1988), no. 2, 223–243. MR 958832, DOI 10.1007/BF01394325
- J.-E. Björk, Rings of differential operators, North-Holland Mathematical Library, vol. 21, North-Holland Publishing Co., Amsterdam-New York, 1979. MR 549189
- Jan-Erik Björk, Filtered Noetherian rings, Noetherian rings and their applications (Oberwolfach, 1983) Math. Surveys Monogr., vol. 24, Amer. Math. Soc., Providence, RI, 1987, pp. 59–97. MR 921079, DOI 10.1090/surv/024/05
- S. C. Coutinho, Modules of codimension one over Weyl algebras, J. Algebra 177 (1995), no. 1, 102–114. MR 1356361, DOI 10.1006/jabr.1995.1287
- S. C. Coutinho, Krull dimension of modules and involutive ideals, Proc. Amer. Math. Soc. 123 (1995), no. 6, 1647–1654. MR 1243163, DOI 10.1090/S0002-9939-1995-1243163-9
- Ofer Gabber, The integrability of the characteristic variety, Amer. J. Math. 103 (1981), no. 3, 445–468. MR 618321, DOI 10.2307/2374101
- V. Ginsburg, Characteristic varieties and vanishing cycles, Invent. Math. 84 (1986), no. 2, 327–402. MR 833194, DOI 10.1007/BF01388811
- Akihiko Gyoja, Theory of prehomogeneous vector spaces without regularity condition, Publ. Res. Inst. Math. Sci. 27 (1991), no. 6, 861–922. MR 1145669, DOI 10.2977/prims/1195169004
- Robin Hartshorne, Algebraic geometry, Graduate Texts in Mathematics, No. 52, Springer-Verlag, New York-Heidelberg, 1977. MR 0463157, DOI 10.1007/978-1-4757-3849-0
- Masaki Kashiwara, $B$-functions and holonomic systems. Rationality of roots of $B$-functions, Invent. Math. 38 (1976/77), no. 1, 33–53. MR 430304, DOI 10.1007/BF01390168
- T. Levasseur, Equidimensionalité de la variété caractéristique, exposé de O. Gabber rédigé par T. Levasseur, unpublished.
- Valery Lunts, Algebraic varieties preserved by generic flows, Duke Math. J. 58 (1989), no. 3, 531–554. MR 1016433, DOI 10.1215/S0012-7094-89-05824-9
- J. C. McConnell and J. C. Robson, Noncommutative Noetherian rings, Pure and Applied Mathematics (New York), John Wiley & Sons, Ltd., Chichester, 1987. With the cooperation of L. W. Small; A Wiley-Interscience Publication. MR 934572
- Gadi Shimon Perets, $d$-critical modules of length $2$ over Weyl algebras, Israel J. Math. 83 (1993), no. 3, 361–368. MR 1239069, DOI 10.1007/BF02784063
Additional Information
- S. C. Coutinho
- Affiliation: Instituto de Matemática, Universidade Federal do Rio de Janeiro, P.O. Box 68530, 21945-970, Rio de Janeiro, RJ, Brazil
- Email: collier@impa.br
- Received by editor(s): February 22, 1996
- © Copyright 1997 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 349 (1997), 3343-3352
- MSC (1991): Primary 16S32; Secondary 16E30, 13N10
- DOI: https://doi.org/10.1090/S0002-9947-97-01901-6
- MathSciNet review: 1407699