Journal of the Ramanujan Mathematical Society

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On the Module of Derivations of Certain Rings of Invariants


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1 Department of Mathematics, IIT Guwahati, Guwahati, Assam, India
     

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Let k be an algebraically closed field of characteristic 0. Let G be a finite cyclic subgroup of GLm(k) having no non-trivial pseudo-reflections. Let R be the ring of invariants obtained by the linear action of G on k[X1, . . . , Xm]. We give an algorithm to find a generating set for Der R. We also give an upper bound for μ(Der R).
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  • [DGPS] W. Decker, G.-M. Greuel, G. Pfister and Schonemann, H., Singular 4-0-2 — A computer algebra system for polynomial computations. http://www.singular.uni-kl.de (2015).

  • [GW08] R. V. Gurjar and V. Wagh, On the number of generators of the module of derivations and multiplicity of certain rings, Journal of Algebra 319 (2008) 2030–2049.

  • [Sage] SageMath, the Sage Mathematics Software System (Version 7.2), The Sage Developers (2016), http://www.sagemath.org.

  • [ST54] G. C. Shephard and J. A. Todd, Finite unitary reflection groups, Canad. J. Math., 6 (1954) 274–304.

  • [Wag06] V. Wagh, On the modules of derivations, the modules of differentials and the multiplicity of certain rings, Ph.D. thesis, Bhaskarachayra Pratishthana, Pune (2006).


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  • On the Module of Derivations of Certain Rings of Invariants

Abstract Views: 255  |  PDF Views: 0

Authors

Arindam Dey
Department of Mathematics, IIT Guwahati, Guwahati, Assam, India
Vinay Wagh
Department of Mathematics, IIT Guwahati, Guwahati, Assam, India

Abstract


Let k be an algebraically closed field of characteristic 0. Let G be a finite cyclic subgroup of GLm(k) having no non-trivial pseudo-reflections. Let R be the ring of invariants obtained by the linear action of G on k[X1, . . . , Xm]. We give an algorithm to find a generating set for Der R. We also give an upper bound for μ(Der R).

References