Stratified modules over an extension algebra
Erzsébet Lukács; András Magyar
Czechoslovak Mathematical Journal (2018)
- Volume: 68, Issue: 2, page 523-551
- ISSN: 0011-4642
Access Full Article
top
Abstract
topHow to cite
topLukács, Erzsébet, and Magyar, András. "Stratified modules over an extension algebra." Czechoslovak Mathematical Journal 68.2 (2018): 523-551. <http://eudml.org/doc/294317>.
@article{Lukács2018,
abstract = {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.},
author = {Lukács, Erzsébet, Magyar, András},
journal = {Czechoslovak Mathematical Journal},
keywords = {standardly stratified algebra; homological dual; standard Koszul algebra},
language = {eng},
number = {2},
pages = {523-551},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Stratified modules over an extension algebra},
url = {http://eudml.org/doc/294317},
volume = {68},
year = {2018},
}
TY - JOUR
AU - Lukács, Erzsébet
AU - Magyar, András
TI - Stratified modules over an extension algebra
JO - Czechoslovak Mathematical Journal
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 68
IS - 2
SP - 523
EP - 551
AB - 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.
LA - eng
KW - standardly stratified algebra; homological dual; standard Koszul algebra
UR - http://eudml.org/doc/294317
ER -
References
top- 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. (1993) Zbl0820.16006MR1265273
- Ágoston, I., Dlab, V., Lukács, E., 10.4153/CJM-1996-046-0, Can. J. Math. 48 (1996), 897-917. (1996) Zbl0868.16009MR1414062DOI10.4153/CJM-1996-046-0
- Ágoston, I., Dlab, V., Lukács, E., Stratified algebras, C. R. Math. Acad. Sci., Soc. R. Can. 20 (1998), 22-28. (1998) Zbl0914.16010MR1619048
- Ágoston, I., Dlab, V., Lukács, E., 10.1023/A:1022373620471, Algebr. Represent. Theory 6 (2003), 97-117. (2003) Zbl1053.16007MR1960515DOI10.1023/A:1022373620471
- Ágoston, I., Dlab, V., Lukács, E., 10.1081/AGB-200060498, Commun. Algebra 33 (2005), 1357-1368. (2005) Zbl1081.16019MR2149063DOI10.1081/AGB-200060498
- Ágoston, I., Happel, D., Lukács, E., Unger, L., 10.1080/00927870008826990, Commun. Algebra 28 (2000), 2745-2752. (2000) Zbl0964.16005MR1757427DOI10.1080/00927870008826990
- Cline, E., Parshall, B., Scott, L., 10.1090/memo/0591, Mem. Am. Math. Soc. 591 (1996). (1996) Zbl0888.16006MR1350891DOI10.1090/memo/0591
- Dlab, V., Quasi-hereditary algebras revisited, An. Ştiinţ. Univ. Ovidius Constanţa, Ser. Mat. 4 (1996), 43-54. (1996) Zbl0873.16008MR1428453
- 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. (1996) Zbl0860.16009MR1388055
- Lukács, E., Magyar, A., 10.1080/00927872.2016.1175609, Commun. Algebra 45 (2017), 1270-1277. (2017) Zbl06715126MR3573378DOI10.1080/00927872.2016.1175609
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.