Article
Full entry |
PDF
(0.4 MB)
Feedback
PDF
(0.4 MB)
Feedback
Keywords:
standardly stratified algebra; homological dual; standard Koszul algebra
standardly stratified algebra; homological dual; standard Koszul algebra
Summary:
Let $A$ be a standard Koszul standardly stratified algebra and $X$ an $A$-module. The paper investigates conditions which imply that the module ${\rm Ext}_A^*(X)$ over the Yoneda extension algebra $A^*$ is filtered by standard modules. In particular, we prove that the Yoneda extension algebra of $A$ is also standardly stratified. This is a generalization of similar results on quasi-hereditary and on graded standardly stratified algebras.
References:
[1] Ágoston, I., Dlab, V., Lukács, E.: Lean quasi-hereditary algebras. Representations of Algebras V. Dlab et al. Proc. of the Sixth International Conf. on Representations of Algebras, Ottawa, 1992, American Mathematical Society, CMS Conf. Proc. 14 (1993), 1-14. MR 1265273 | Zbl 0820.16006
[2] Ágoston, I., Dlab, V., Lukács, E.: Homological duality and quasi-heredity. Can. J. Math. 48 (1996), 897-917. DOI 10.4153/CJM-1996-046-0 | MR 1414062 | Zbl 0868.16009
[3] Ágoston, I., Dlab, V., Lukács, E.: Stratified algebras. C. R. Math. Acad. Sci., Soc. R. Can. 20 (1998), 22-28. MR 1619048 | Zbl 0914.16010
[4] Ágoston, I., Dlab, V., Lukács, E.: Quasi-hereditary extension algebras. Algebr. Represent. Theory 6 (2003), 97-117. DOI 10.1023/A:1022373620471 | MR 1960515 | Zbl 1053.16007
[5] Ágoston, I., Dlab, V., Lukács, E.: Standardly stratified extension algebras. Commun. Algebra 33 (2005), 1357-1368. DOI 10.1081/AGB-200060498 | MR 2149063 | Zbl 1081.16019
[6] Ágoston, I., Happel, D., Lukács, E., Unger, L.: Finitistic dimension of standardly stratified algebras. Commun. Algebra 28 (2000), 2745-2752. DOI 10.1080/00927870008826990 | MR 1757427 | Zbl 0964.16005
[7] Cline, E., Parshall, B., Scott, L.: Stratifying Endomorphism Algebras. Mem. Am. Math. Soc. 591 (1996). DOI 10.1090/memo/0591 | MR 1350891 | Zbl 0888.16006
[8] Dlab, V.: Quasi-hereditary algebras revisited. An. Ştiinţ. Univ. Ovidius Constanţa, Ser. Mat. 4 (1996), 43-54. MR 1428453 | Zbl 0873.16008
[9] Green, E. L., Martínez-Villa, R.: Koszul and Yoneda algebras. Representation Theory of Algebras R. Bautista Seventh international Conf., Mexico, 1994, American Mathematical Society. CMS Conf. Proc. 18 (1996), 247-297. MR 1388055 | Zbl 0860.16009
[10] Lukács, E., Magyar, A.: Standard Koszul standardly stratified algebras. Commun. Algebra 45 (2017), 1270-1277. DOI 10.1080/00927872.2016.1175609 | MR 3573378 | Zbl 06715126
Search
Partner of
