Derived dimension via τ -tilting theory

Yingying Zhang

Czechoslovak Mathematical Journal (2021)

  • Volume: 71, Issue: 4, page 1167-1172
  • ISSN: 0011-4642

Abstract

top
Comparing the bounded derived categories of an algebra and of the endomorphism algebra of a given support τ -tilting module, we find a relation between the derived dimensions of an algebra and of the endomorphism algebra of a given τ -tilting module.

How to cite

top

Zhang, Yingying. "Derived dimension via $\tau $-tilting theory." Czechoslovak Mathematical Journal 71.4 (2021): 1167-1172. <http://eudml.org/doc/297981>.

@article{Zhang2021,
abstract = {Comparing the bounded derived categories of an algebra and of the endomorphism algebra of a given support $\tau $-tilting module, we find a relation between the derived dimensions of an algebra and of the endomorphism algebra of a given $\tau $-tilting module.},
author = {Zhang, Yingying},
journal = {Czechoslovak Mathematical Journal},
keywords = {support $\tau $-tilting module; endomorphism algebra; derived dimension},
language = {eng},
number = {4},
pages = {1167-1172},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Derived dimension via $\tau $-tilting theory},
url = {http://eudml.org/doc/297981},
volume = {71},
year = {2021},
}

TY - JOUR
AU - Zhang, Yingying
TI - Derived dimension via $\tau $-tilting theory
JO - Czechoslovak Mathematical Journal
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 71
IS - 4
SP - 1167
EP - 1172
AB - Comparing the bounded derived categories of an algebra and of the endomorphism algebra of a given support $\tau $-tilting module, we find a relation between the derived dimensions of an algebra and of the endomorphism algebra of a given $\tau $-tilting module.
LA - eng
KW - support $\tau $-tilting module; endomorphism algebra; derived dimension
UR - http://eudml.org/doc/297981
ER -

References

top
  1. Adachi, T., Iyama, O., Reiten, I., 10.1112/S0010437X13007422, Compos. Math. 150 (2014), 415-452. (2014) Zbl1330.16004MR3187626DOI10.1112/S0010437X13007422
  2. Hügel, L. Angeleri, Marks, F., Vitória, J., 10.1093/imrn/rnv191, Int. Math. Res. Not. 2016 (2016), 1251-1284. (2016) Zbl1367.16005MR3493448DOI10.1093/imrn/rnv191
  3. Assem, I., Simson, D., Skowroński, A., 10.1017/CBO9780511614309, London Mathematical Society Student Texts 65. Cambridge University Press, Cambridge (2006). (2006) Zbl1092.16001MR2197389DOI10.1017/CBO9780511614309
  4. Bekkert, V., Merklen, H. A., 10.1023/a:1025142023594, Algebr. Represent. Theory 6 (2003), 285-302. (2003) Zbl1032.16011MR2000963DOI10.1023/a:1025142023594
  5. Burban, I., Drozd, Y., On the derived categories of gentle and skew-gentle algebra: Homological algebra and matrix problems, Available at https://arxiv.org/abs/1706.08358 (2017), 57 pages. (2017) 
  6. Chen, X.-W., Ye, Y., Zhang, P., 10.1080/00927870701649184, Commun. Algebra 36 (2008), 1-10. (2008) Zbl1135.16012MR2378361DOI10.1080/00927870701649184
  7. Han, Y., Derived dimensions of representation-finite algebras, Available at https://arxiv.org/abs/0909.0330 (2009), 4 pages. (2009) 
  8. Happel, D., 10.1007/BF02564452, Comment. Math. Helv. 62 (1987), 339-389. (1987) Zbl0626.16008MR0910167DOI10.1007/BF02564452
  9. Oppermann, S., 10.1215/00127094-2009-025, Duke Math. J. 148 (2009), 211-249. (2009) Zbl1173.16007MR2524495DOI10.1215/00127094-2009-025
  10. Rouquier, R., 10.1007/s00222-006-0499-7, Invent. Math. 165 (2006), 357-367. (2006) Zbl1101.18006MR2231960DOI10.1007/s00222-006-0499-7
  11. Rouquier, R., 10.1017/is007011012jkt010, J. -Theory 1 (2008), 193-256. (2008) Zbl1165.18008MR2434186DOI10.1017/is007011012jkt010
  12. Suarez, P., 10.1016/j.jpaa.2021.106740, J. Pure Appl. Algebra 225 (2021), 106740. (2021) MR4232685DOI10.1016/j.jpaa.2021.106740
  13. Treffinger, H., 10.1016/j.jalgebra.2017.03.004, J. Algebra 481 (2017), 362-392. (2017) Zbl1411.16012MR3639480DOI10.1016/j.jalgebra.2017.03.004
  14. Zheng, J., Huang, Z., 10.1016/j.jalgebra.2020.04.012, J. Algebra 556 (2020), 1211-1228. (2020) Zbl1440.18025MR4090423DOI10.1016/j.jalgebra.2020.04.012

NotesEmbed ?

top

You 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.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.