174
Views
3
CrossRef citations to date
0
Altmetric
Original Articles

Orthogonal invariants of skew-symmetric matrices

Pages 851-862 | Received 20 Apr 2010, Accepted 11 Jul 2010, Published online: 14 Apr 2011

References

  • Aslaksen , H , Tan , E-C and Zho , C-B . 1995 . Invariant theory of special orthogonal groups . Pac. J. Math. , 168 : 207 – 215 .
  • Derksen , H and Weyman , J . 2002 . Generalized quivers associated to reductive groups . Colloq. Math. , 94 : 151 – 173 .
  • Domokos , M , Kuzmin , SG and Zubkov , AN . 2002 . Rings of matrix invariants in positive characteristic . J. Pure Appl. Algebra , 176 : 61 – 80 .
  • Donkin , S . 1992 . Invariants of several matrices . Invent. Math. , 110 : 389 – 401 .
  • Drensky , V and Sadikova , L . 2006 . Generators of invariants of two 4 × 4 matrices . C. R. Acad. Bulgare Sci. , 59 : 477 – 484 .
  • Gantmacher , FR . 1959 . The Theory of Matrices , Vol. 2 , 276 New York : AMS Chelsea Publishing .
  • Hashimoto , M . 2001 . Good filtrations of symmetric algebras and strong F-regularity of invariant subrings . Math. Z. , 236 : 605 – 623 .
  • Hilbert , D . 1893 . Über die vollen invariantensysteme . Math. Ann. , 42 : 313 – 373 .
  • Hilbert , D . 1970 . “ Über die vollen invariantensysteme ” . In Ges. Abh., II , Berlin : Springer-Verlag .
  • Kraft , H . 1985 . Geometrische Methoden in der Invariantentheorie , Braunschweig, Wiesbaden : Friedr. Vieweg & Sohn .
  • Lopatin , AA . 2004 . The invariant ring of triples of 3 × 3 matrices over a field of arbitrary characteristic . Sibirsk. Mat. Zh. , 45 : 624 – 633 . (Russian) (English translation: Siberian Math. J. 45 (2004), pp. 513–521)
  • Lopatin , AA . 2004 . The algebra of invariants of 3 × 3 matrices over a field of arbitrary characteristic . Comm. Algebra , 32 : 2863 – 2883 .
  • Lopatin , AA . 2005 . Relatively free algebras with the identity x 3 = 0 . Comm. Algebra , 33 : 3583 – 3605 .
  • Lopatin , AA . 2009 . Invariants of quivers under the action of classical groups . J. Algebra , 321 : 1079 – 1106 .
  • Lopatin , AA . Relations between O(n)-invariants of several matrices , submitted, arXiv: 0902.4266
  • Lopatin , AA . On minimal generating systems for matrix O(3)-invariants , to appear in Linear Multilinear Algebra, arXiv: 0902.4270
  • Procesi , C . 1976 . The invariant theory of n × n matrices . Adv. Math. , 19 : 306 – 381 .
  • Procesi , C . 1984 . Computing with 2 × 2 matrices . J. Algebra , 87 : 342 – 359 .
  • Sibirskii , KS . 1968 . Algebraic invariants of a system of matrices . Sibirsk. Mat. Zh. , 9 : 152 – 164 . (Russian)
  • Teranishi , Y . 1986 . The ring of invariants of matrices . Nagoya Math. J. , 104 : 149 – 161 .
  • Teranishi , Y . 1988 . The Hilbert series of rings of matrix concomitants . Nagoya Math. J. , 111 : 143 – 156 .
  • Wellstein , J . 1930 . Über symmetrische, alternierende und orthogonale Normalformen von Matrizen . J. Reine Angew. Math. , 163 : 166 – 182 .
  • Zubkov , AN . 1996 . On a generalization of the Razmyslov–Procesi theorem . Algebra Logic , 35 : 241 – 254 .
  • Zubkov , AN . 1999 . Invariants of an adjoint action of classical groups . Algebra Logic , 38 : 299 – 318 .
  • Zubkov , AN . 2005 . Invariants of mixed representations of quivers I . J. Algebra Appl. , 4 : 245 – 285 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.