headerpos: 12198
 
 
 

Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952

Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952
Publisher
Journal Information
» Editorial Board
» Editorial Policy
» Archival Policy
» Article Publication Charges
» Copyright and Licensing Policy
Guidelines for Authors
» For Authors
» Instructions to Authors
» LaTex style files
Guidelines for Reviewers
» For Reviewers
» Review Form
Open Access
List of Issues
» 2019
» 2018
» 2017
» 2016
» 2015
» 2014
» 2013
» 2012
» 2011
» 2010
Vol. 59, Issue 4
Vol. 59, Issue 3
Vol. 59, Issue 2
Vol. 59, Issue 1
» 2009
» 2008
» Back Issues Phys. Math.
» Back Issues Chemistry
» Back issues (full texts)
  in Google. Phys. Math.
» Back issues (full texts)
  in Google. Chemistry
» Back issues (full texts)
  in Google Engineering
» Back issues (full texts)
  in Google Ecology
» Back issues in ETERA Füüsika, Matemaatika jt
Subscription Information
» Prices
Internet Links
Support & Contact
Publisher
» Staff
» Other journals

Group actions, orbit spaces, and noncommutative deformation theory; pp. 364–369

(Full article in PDF format) doi: 10.3176/proc.2010.4.16


Authors

Arvid Siqveland

Abstract

Consider the action of a group G on an ordinary commutative k-variety X = Spec(A). In this note we define the category of AG-modules and their deformation theory. We then prove that this deformation theory is equivalent to the deformation theory of modules over the noncommutative k-algebra A[G] = A#G. The classification of orbits can then be studied over a commutative ring, and we give an example of this on surface cyclic singularities.

Keywords

A–G-module, noncommutative deformation theory, noncommutative blowup, cyclic surface singularities, orbit closures, swarm of modules, r-pointed artinian k-algebras, noncommutative deformation functor, Generalized Matric Massey Products (GMMP), McKay correspondence.

References

1. Eriksen , E. An introduction to noncommutative deformations of modules. Lect. Notes Pure Appl. Math. , 2005 , 243(2) , 90–126.
doi:10.1201/9781420028102.ch5

2. Laudal , O. A. Matric Massey products and formal moduli I. In Algebra , Algebraic Topology and Their Interactions (Roos , J.-E. , ed.). Lecture Notes in Math. , 1183 , 218–240. Springer Verlag , 1986.

3. Laudal , O. A. Noncommutative deformations of modules. Homology Homotopy Appl. , 2002 , 4(2) , 357–396.

4. Laudal , O. A. Noncommutative algebraic geometry. Rev. Mat. Iberoamericana , 2003 , 19(2) , 509–580.

5. Siqveland , A. The method of computing formal moduli. J. Algebra , 2001 , 241 , 292–327.
doi:10.1006/jabr.2001.8757

6. Siqveland , A. Global Matric Massey products and the compactified Jacobian of the E6-singularity. J. Algebra , 2001 , 241 , 259–291.
doi:10.1006/jabr.2001.8758

7. Siqveland , A. A standard example in noncommutative deformation theory. J. Gen. Lie Theory Appl. , 2008 , 2(3) , 251–255.
 
Back

Current Issue: Vol. 68, Issue 4, 2019




Publishing schedule:
No. 1: 20 March
No. 2: 20 June
No. 3: 20 September
No. 4: 20 December