Generalized Green correspondence of graded modules

Abstract

The author studies the Green correspondence and quasi-Green correspondence for indecomposable modules over strongly graded rings. The motivation is to investigate the influence of induction and restriction processes on indecomposability of graded modules.

Keywords

Vertices / Sources / Graded rings / Graded modules / Green correspondence

References

[1] Burry D. W.. A strengthened theory of vertices and sources. J. Algebra, 1979, 59(2): 330-344

[2] Curtis C. W., Reiner I.. Methods of Representation Theory, Vol. I, 1981, New York: John Wiley

[3] Dade E. C.. Group-graded rings and modules. Math. Z., 1980, 174(3): 241-262

[4] Green J. A.. On the indecomposable representations of a finite group. Math. Z., 1958, 70(1): 430-445

[5] Green J. A.. A transfer theorem for modular representations. J. Algebra, 1964, 1(1): 73-84

[6] Héthelyi L., Szöke M., Lux K.. The restriction of indecomposable modules for group algebras and the quasi-Green correspondence. Comm. Algebra, 1998, 26(1): 83-95

[7] Héthelyi L., Szöke M.. Green correspondence and its generalizations. Comm. Algebra, 2000, 28(9): 4463-4479

[8] Hussein S. S.. Induced and restricted modules over graded rings. Proc. Math. Phys. Soc. Egypt, 2001, 76: 1-13

[9] Hussein, S. S., Vertices and sources of indecomposable graded modules, J. Egyptian Math. Soc., to appear.

[10] Landrock P., Michler G. O.. Block structure of the smallest Janko group. Math. Ann., 1978, 232(3): 205-238

[11] Năstăsescu C., van Oystaeyen F.. Graded Ring Theory, Mathematical Library, 1982, Amsterdam: North-Holand 28

[12] Năstăsescu C., van Oystaeyen F.. Dimensions of Ring Theory, 1987, Boston: D. Reidel Publ. Co.