175
Views
6
CrossRef citations to date
0
Altmetric
Original Articles

The graded Gelfand--Kirillov dimension of verbally prime algebras

Pages 1433-1450 | Received 30 Oct 2010, Accepted 29 Jan 2011, Published online: 20 Apr 2011

References

  • Azevedo , SS , Fidelis , M and Koshlukov , P . 2005 . Graded identities and PI equivalence of algebras in positive characteristic . Commun. Algebra , 33 : 1011 – 1022 .
  • Balaba , IN . 2005 . Graded prime PI-algebras . J. Math. Sci. , 128 : 3345 – 3349 .
  • Berele , A . 1988 . Cocharacters of Z/2Z-graded algebras . Israel J. Math. , 61 : 225 – 234 .
  • Berele , A . 1993 . Generic verbally prime PI-algebras and their GK-dimensions . Commun. Algebra , 21 : 1487 – 1504 .
  • Centrone , L . A note on graded Gelfand--Kirillov dimension of graded algebras . J. Algebra Appl. , (to appear)
  • Di Vincenzo , OM . 1996 . Cocharacters of G-graded algebras . Commun. Algebra , 24 : 3293 – 3310 .
  • Di Vincenzo , OM , Drensky , V and Nardozza , V . 2004 . Algebras satisfying the polynomial identity [x 1, x 2][x 3, x 4, x 5] = 0 . J. Algebra Appl. , 3 : 121 – 142 .
  • Di Vincenzo , OM and Nardozza , V . 2003 . Graded polynomial identities for tensor products by the Grassmann algebra . Commun. Algebra , 31 : 1453 – 1474 .
  • Drensky , V . 1987 . Extremal varieties of algebras I (Russian) . Serdica , 13 : 320 – 332 .
  • Drensky , V and Formanek , E . 2000 . Polynomial Identity Rings , Basel, Boston, Berlin : Birkhauser Verlag .
  • Drensky , V and Giambruno , A . 1994 . Cocharacters, codimensions and Hilbert series of the polynomial identities for 2 × 2 matrices with involution . Can. J. Math , 46 : 718 – 733 .
  • Isaacs , IM . 1976 . Character Theory of Finite Groups, Pure and Applied Mathematics , Vol. 69 , New York : Academic Press .
  • Kemer , AR . 1984 . Varieties and ℤ2-graded algebras (Russian), Izv. Akad. Nauk SSSR . Ser. Mat. , 48 : 1042 – 1059 . (Translation: Math. USSR, Izv. 25 (1985), 359--374)
  • Kerber , A . 1971 . Representations of Permutation Groups, Lecture Notes in Mathematics , Vol. 240 , Berlin, Heidelberger, New York : Springer-Verlag .
  • Krause , GR and Lenagan , TH . 2000 . Growth of Algebras and Gelfand--Kirillov Dimension, Revised Edition, Graduate Studies in Mathematics , Vol. 22 , Providence , RI : American Mathematical Society .
  • Lewin , J . 1974 . A matrix representation for associative algebras I . Trans. Amer. Math. Soc. , 188 : 293 – 308 .
  • McConnell , JC and Robson , JC . 1987 . Noncommutative Noetherian Rings, Pure and Applied Mathematics , New York : Wiley Interscience .
  • Nǎstǎsescu , C and van Oystaeyen , F . 1982 . Graded Ring Theory , Amsterdam : North Holland .
  • Procesi , C . 1967 . Non-commutative affine rings . Atti Accad. Naz. Lincei Mem. Cl. Sci. Fis. Mat. Natur. Sez. I , 8 : 237 – 255 .
  • Sagan , BE . 2000 . The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions, Graduate Texts in Mathematics , Vol. 203 , Berlin : Springer Verlag .
  • Vasilovsky , SY . 1999 . ℤ n -graded polynomial identities of the full matrix algebra of order n . Proc. Amer. Math. Soc. , 127 : 3517 – 3524 .

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.