Automorphisms and ideals of the Weyl algebra

Mathematische Annalen

Volumn 318, Issue 1, 2000, Pages 127-147

  Berest, Yuri ^a   Wilson, George ^b  

^a Cornell University ^*  (United States)

^b IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034409311     PISSN: 00255831     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002080000115     Document Type: Article

References (31)

1. I.V. Artamkin, Action of biregular automorphisms of the affine plane on pairs of matrices, Math. USSR Izvestiya 33 (1989), 433-439
2. E. Arbarello, C. De Concini, V. G. Kac and C. Procesi, Moduli space of curves and representation theory, Comm. Math. Phys. 117 (1988), 1-36
3. Yu. Berest and G. Wilson, Classification of rings of differential operators on affine curves, IMRN 2 (1999), 105-109
4. Yu. Berest and G. Wilson, Ideal classes of the Weyl algebra and noncommutative projective geometry, in preparation
5. O. Biquard, Sur les équations de Nahm et la structure de Poisson des algèbres de Lie semi-simples complexes, Math. Ann. 304 (1996), 253-276
6. R. C. Cannings and M. P. Holland, Right ideals in rings of differential operators, J. Algebra 167 (1994), 116-141
7. A. J. Czerniakiewicz, Automorphisms of a free associative algebra of rank 2. II, Trans. Amer. Math. Soc. 160 (1972), 309-315
8. J. Dixmier, Sur les algèbres de Weyl, Bull. Soc. Math. France 96 (1968), 209-242
9. V. Ginzburg, Noncommutative symplectic geometry and Calogero-Moser space, preprint (1999)
10. M. Hazewinkel and S. I. Marcus, On Lie algebras and finite dimensional filtering, Stochastics 7 (1982), 29-62
11. H. W. E. Jung, Über ganze birationale Transformationen der Ebene, J. Reine Angew. Math. 184 (1942), 161-174
12. K. M. Kouakou, Isomorphismes entre algèbres d'opérateurs différentiels sur les courbes algébriques affines, Thèse, Université Claude Bernard-Lyon 1 (1994)
13. A. G. Kovalev, Nahm's equation and complex adjoint orbits, Quart. J. Math. Oxford Ser. (2) 47 (1996), 41-58
14. I. M. Krichever, Integration of nonlinear equations by methods of algebraic geometry, Funct. Anal. Appl. 11(1) (1977), 12-26
15. P. B. Kronheimer, A hyper-Kählerian structure on coadjoint orbits of a semisimple complex group, J. London Math. Soc. (2) 42 (1990), 193-208
16. L. Le Bruyn, Moduli spaces for right ideals of the Weyl algebra, J. Algebra 172 (1995), 32-48
17. G. Letzter and L. Makar-Limanov, Rings of differential operators over rational affine curves, Bull. Soc. Math. France 118 (1990), 193-209
18. I. G. Macdonald, Symmetric functions and Hall polynomials, Oxford University Press 1979; second edition 1995
19. L. Makar-Limanov, On automorphism of free algebras with two generators, Funct. Anal. Appl. 4 (1970), 262-264
20. L. Makar-Limanov, On automorphisms of Weyl algebra, Bull. Soc. Math. France 112 (1984), 359-363
21. J. C. McConnell and J. C. Robson, Noncommutative Noetherian Rings, J. Wiley & Sons, New York, 1987
22. H. Nakajima, Lectures on Hilbert schemes of points on surfaces, University Lecture Series 18, Amer. Math. Society, Providence RI, 1999
23. I. Schur, Über vertauschbare lineare Differentialausdrücke, Sitzungsber. Berliner Math. Ges. 4 (1905), 2-8; Gesammelte Abhandlungen Band I, Berlin-Heidelberg-New York (1973), 170-176
24. I. Schur, Über vertauschbare lineare Differentialausdrücke, Sitzungsber. Berliner Math. Ges. 4 (1905), 2-8; Gesammelte Abhandlungen Band I, Berlin-Heidelberg-New York (1973), 170-176
25. I. R. Shafarevich, On some infinite-dimensional groups. II, Math. USSR Izvestija 18 (1982), 185-194
26. J. T. Stafford, The Weyl algebra and finite dimensional filtering, Stochastics 14, (1984), 29-31
27. J. T. Stafford, Endomorphisms of right ideals in the Weyl algebra, Trans. Amer. Math. Soc. 299 (1987), 624-639
28. G. Segal and G. Wilson, Loop groups and equations of KdV type, Publ. Math. I.H.E.S. 61, (1985), 5-65
29. G. Wilson, Bispectral commutative ordinary differential operators, J. Reine Angew. Math. 442 (1993), 177-204
30. G. Wilson, Collisions of Calogero-Moser particles and an adelic Grassmannian (with an Appendix by I. G. Macdonald), Invent. Math. 133 (1998), 1-41
31. G. Wilson, Bispectral symmetry, the Weyl algebra and differential operators on curves, Proceedings of the Steklov Mathematical Institute 225 (1999), 141-147