Abelian Gradings on Upper Block Triangular Matrices
Canadian mathematical bulletin, Tome 55 (2012) no. 1, pp. 208-213

Voir la notice de l'article provenant de la source Cambridge University Press

Let $G$ be an arbitrary finite abelian group. We describe all possible $G$ -gradings on upper block triangular matrix algebras over an algebraically closed field of characteristic zero.
DOI : 10.4153/CMB-2011-048-4
Mots-clés : 16W50, gradings, upper block triangular matrices
Valenti, Angela; Zaicev, Mikhail. Abelian Gradings on Upper Block Triangular Matrices. Canadian mathematical bulletin, Tome 55 (2012) no. 1, pp. 208-213. doi: 10.4153/CMB-2011-048-4
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[1] [1] Bahturin, Y. A., Montgomery, S., and Zaicev, M. V., Generalized Lie solvability of associative algebras. In: Groups, Rings, Lie and Hopf Algebras. Math. Appl. 555, Kluwer, Dordrecht, 2003, pp. 1–23 Google Scholar

[2] [2] Bahturin, Y. A., Sehgal, S. K., and Zaicev, M. V., Group gradings on associative algebras. J. Algebra 241(2001), no. 2, 677–698. doi:10.1006/jabr.2000.8643 Google Scholar

[3] [3] Bahturin, Y. A., Shestakov, I., and Zaicev, M. V., Gradings on simple Jordan algebras and Lie algebras. J. Algebra 283(2005), 849–868. doi:10.1016/j.jalgebra.2004.10.007 Google Scholar

[4] [4] Bahturin, Y. A. and Zaicev, M. V., Group gradings on matrix algebras. Dedicated to Robert V. Moody. Canad. Math. Bull. 45 (2002), no. 4, 499–508. doi:10.4153/CMB-2002-051-x Google Scholar

[5] [5] Bahturin, Y. A. and Zaicev, M. V., Identities of graded algebras and codimension growth. Trans. Amer. Math. Soc. 356(2004), no. 10, 3939–3950. doi:10.1090/S0002-9947-04-03426-9 Google Scholar

[6] [6] Di Vincenzo, O. M., Koshlukov, P., and Valenti, A., Gradings on the algebra of upper triangular matrices and their graded identities. J. Algebra 275(2004), no. 2, 550–556. doi:10.1016/j.jalgebra.2003.08.004 Google Scholar

[7] [7] Giambruno, A. and Zaicev, M., Polynomial Identities and Asymptotic Methods. Mathematical Surveys and Monographs 122, American Mathematical Society, Providence, RI, 2005. Google Scholar

[8] [8] Jacobson, N., The Theory of Rings American Mathematical Society Math. Surveys 2, American Mathematical Society, New York, 1943. Google Scholar

[9] [9] Kantor, I. L., Some generalizations of Jordan algebras. Trudy Sem. Vektor. Tenzor. Anal. 16(1972), 407–499. Google Scholar

[10] [10] Sehgal, S. K., Topics in Group Rings. Monographs and Textbooks in Pure and Applied Math. 50, Marcel Dekker, New York, 1978. Google Scholar

[11] [11] Sehgal, S. K. and Zaicev, M. V., Graded identities and induced gradings on group algebras. In: Groups, Rings, Lie and Hopf Algebras, Mathematics Appl. 555, Kluwer Acad. Public. 2003, pp. 211–219. Google Scholar

[12] [12] Smirnov, O. N., Simple associative algebras with finite -grading. J. Algebra 196(1997), 171–184. doi:10.1006/jabr.1997.7087 Google Scholar

[13] [13] Smirnov, O. N., Finite -grading of Lie algebras and symplectic involution. J. Algebra 218(1999), no. 1, 246–275. doi:10.1006/jabr.1999.7880 Google Scholar

[14] [14] Valenti, A. and Zaicev, M. V., Abelian gradings on upper-triangular matrices. Arch. Math. 80(2003), no. 1, 12–17. Google Scholar

[15] [15] Valenti, A. and Zaicev, M. V., Group gradings on upper triangular matrices. Arch. Math. 89(2007), no. 1, 33–40. Google Scholar

[16] [16] Zaĭtsev, M. V. and Segal, S. K., Finite gradings of simple Artinian rings. (Russian) Vestnik Moskov. Univ. Ser. I Mat. Mekh. (2001) no. 3, 21–24; translation in Moscow Univ. Math. Bull. 56(2001), no. 3, 21–24. Google Scholar

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