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Characteristic polynomials of finitely generated modules over Weyl algebras

Published online by Cambridge University Press:  17 April 2009

Alexander B. Levin
Affiliation:
Department of Mathematics, The Catholic University of America, Washington DC 20064, United States of America, e-mail: levin@cua.edu
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Abstract

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In this paper we modify the classical Gröbner basis technique and prove the existence of a characteristic polynomial in two variables associated with a finitely generated module over a Weyl algebra. We determine invariants of such a polynomial and show that some of the invariants are not carried by the Bernstein dimension polynomial of the module.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2000

References

REFERENCES

[1]Becker, T. and Weispfenning, V., Gröbner bases. A computational approach to commutative algebra (Springer-Verlag, Berlin, Heidelberg, New York, 1993).Google Scholar
[2]Bernstein, I.N., ‘Modules over the ring of differential operators. A study of the fundamental solutions of equations with constant coefficients, Functional Anal. Appl. 5 (1971), 89101.CrossRefGoogle Scholar
[3]Bernstein, I.N., ‘The analytic continuation of generalized functions with respect to a parameter, Functional Anal. Appl. 6 (1972), 273285.CrossRefGoogle Scholar
[4]Björk, J.- E., Rings of differential operators (North Holland Publishing Company, Amsterdam, New York, 1979).Google Scholar
[5]Cameron, P.J., Combinatorics. Topics, techniques, algorithms (Cambridge University Press, Cambridge, 1994).Google Scholar
[6]Eisenbud, D., Commutative algebra with a view toward algebraic geometry (Springer-Verlag, Berlin, Heidelberg, New York, 1995).Google Scholar
[7]Insa, M. and Pauer, F., ‘Gröbner bases in rings of differential operators’, in Gröbner Bases and Applications (Cambridge Univ. Press, New York, 1998), pp. 367380.CrossRefGoogle Scholar
[8]Kolchin, E.R., Differential algebra and algebraic groups (Academic Press, New York, 1973).Google Scholar
[9]Kondrateva, M.V., Levin, A.B., Mikhalev, A.V. and Pankratev, E. V., ‘Computation of dimension polynomials, Internat. J. Algebra Comput. 2 (1992), 117137.CrossRefGoogle Scholar
[10]Kondrateva, M.V., Levin, A.B., Mikhalev, A.V. and Pankratev, E.V., Differential and difference dimension polynomials (Kluwer Academic Publishers, Dordrecht, Boston, London, 1999).CrossRefGoogle Scholar