Endomorphism algebras of exceptional sequences over path algebras of type A ˜ n

Ibrahim Assem; Yingbo Zhang

Colloquium Mathematicae (1998)

  • Volume: 77, Issue: 2, page 271-292
  • ISSN: 0010-1354

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Assem, Ibrahim, and Zhang, Yingbo. "Endomorphism algebras of exceptional sequences over path algebras of type $\widetilde{A}_{n}$." Colloquium Mathematicae 77.2 (1998): 271-292. <http://eudml.org/doc/210590>.

@article{Assem1998,
author = {Assem, Ibrahim, Zhang, Yingbo},
journal = {Colloquium Mathematicae},
keywords = {gentle algebras; exceptional sequences and their endomorphism algebras; tilted algebras; exceptional sequences; hereditary algebras of type ; Auslander-Reiten quivers; quivers; path algebras; endomorphism algebras; representation finite algebras},
language = {eng},
number = {2},
pages = {271-292},
title = {Endomorphism algebras of exceptional sequences over path algebras of type $\widetilde\{A\}_\{n\}$},
url = {http://eudml.org/doc/210590},
volume = {77},
year = {1998},
}

TY - JOUR
AU - Assem, Ibrahim
AU - Zhang, Yingbo
TI - Endomorphism algebras of exceptional sequences over path algebras of type $\widetilde{A}_{n}$
JO - Colloquium Mathematicae
PY - 1998
VL - 77
IS - 2
SP - 271
EP - 292
LA - eng
KW - gentle algebras; exceptional sequences and their endomorphism algebras; tilted algebras; exceptional sequences; hereditary algebras of type ; Auslander-Reiten quivers; quivers; path algebras; endomorphism algebras; representation finite algebras
UR - http://eudml.org/doc/210590
ER -

References

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  1. [A1] Assem, I.: Tilted algebras of type A n , Comm. Algebra 10 (1982) 2121- 2139. Zbl0495.16028
  2. [A2] Assem, Tilting theory - an introduction, in: Topics in Algebra, Banach Center Publ. 26, Part 1, PWN, Warszawa, 1990, 127-180. 
  3. [AH] I. Assem and Happel, D.: Generalized tilted algebras of type A n , Comm. Algebra 9 (1981), 2101-2125. Zbl0481.16009
  4. [AS] I. Assem and Skowroński, A.: Iterated tilted algebras of type ˜ A n , Math. Z. 195 (1987), 269-290. Zbl0601.16022
  5. [ARS] M. Auslander, I. Reiten and Smalο, S. O.: Representation Theory of Artin Algebras, Cambridge Stud. Adv. Math. 36, Cambridge Univ. Press, 1995. 
  6. [B] Bondal, A. I.: Representations of associative algebras and coherent sheaves, Izv. Akad. Nauk SSSR Ser. Mat. 53 (1989), 25-44 (in Russian); English transl.: Math. USSR-Izv. 34 (1990), 23-45. 
  7. [BR] M. Butler and Ringel, C. M.: Auslander-Reiten sequences with few middle terms and applications to string algebras, Comm. Algebra 15 (1987), 145-179. Zbl0612.16013
  8. [CB] Crawley-Boevey, W.: Exceptional sequences of representations of quivers, in: Representations of Algebras, Sixth Internat. Conf., Ottawa, 1992, CMS Conf. Proc. 14, Amer. Math. Soc., 1993, 117-124. Zbl0828.16012
  9. [DR] V. Dlab and Ringel, C. M.: Indecomposable representations of graphs and algebras, Mem. Amer. Math. Soc. 173 (1976). 
  10. [GR] A. L. Gorodentsev and Rudakov, A. N.: Exceptional vector bundles on projective spaces, Duke Math. J. 54 (1987), 115-130. Zbl0646.14014
  11. [H] Huard, F.: Tilted gentle algebras, Comm. Algebra 26 (1998), 63-72. Zbl0898.16010
  12. [K] Kerner, O.: Representations of wild quivers, in: Representation Theory of Algebras and Related Topics, Seventh Internat. Conf., Mexico, 1994, CMS Conf. Proc. 19, Amer. Math. Soc., 1996, 65-107. Zbl0863.16010
  13. [M] Meltzer, H.: Exceptional sequences and tilting complexes for hereditary algebras of type A n , preprint, 1996. 
  14. [R1] Ringel, C. M.: Tame Algebras and Integral Quadratic Forms, Lecture Notes in Math. 1099, Springer, 1984. 
  15. [R2] Ringel, C. M.: The braid group action on the set of exceptional sequences of a hereditary artin algebra, in: Abelian Group Theory and Related Topics (Oberwolfach, 1993), Contemp. Math. 171, Amer. Math. Soc., 1994, 339-352. Zbl0851.16010
  16. [R] Roldán, O.: Tilted algebras of type n, ˜ B n , ˜ C n and ˜ B C n , Ph.D. thesis, Carleton Univ., 1983. 
  17. [Y] Yao, H.: Endomorphism algebras of exceptional sequences of type A n , Algebra Colloq. 3 (1996), 25-32. 

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