Derived equivalences between generalized matrix algebras

QingHua Chen; HongJin Liu

Czechoslovak Mathematical Journal (2020)

  • Volume: 70, Issue: 1, page 147-160
  • ISSN: 0011-4642

Abstract

top
We construct derived equivalences between generalized matrix algebras. We record several corollaries. In particular, we show that the n -replicated algebras of two derived equivalent, finite-dimensional algebras are also derived equivalent.

How to cite

top

Chen, QingHua, and Liu, HongJin. "Derived equivalences between generalized matrix algebras." Czechoslovak Mathematical Journal 70.1 (2020): 147-160. <http://eudml.org/doc/297038>.

@article{Chen2020,
abstract = {We construct derived equivalences between generalized matrix algebras. We record several corollaries. In particular, we show that the $n$-replicated algebras of two derived equivalent, finite-dimensional algebras are also derived equivalent.},
author = {Chen, QingHua, Liu, HongJin},
journal = {Czechoslovak Mathematical Journal},
keywords = {derived equivalence; tilting complex; generalized matrix algebra},
language = {eng},
number = {1},
pages = {147-160},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Derived equivalences between generalized matrix algebras},
url = {http://eudml.org/doc/297038},
volume = {70},
year = {2020},
}

TY - JOUR
AU - Chen, QingHua
AU - Liu, HongJin
TI - Derived equivalences between generalized matrix algebras
JO - Czechoslovak Mathematical Journal
PY - 2020
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 70
IS - 1
SP - 147
EP - 160
AB - We construct derived equivalences between generalized matrix algebras. We record several corollaries. In particular, we show that the $n$-replicated algebras of two derived equivalent, finite-dimensional algebras are also derived equivalent.
LA - eng
KW - derived equivalence; tilting complex; generalized matrix algebra
UR - http://eudml.org/doc/297038
ER -

References

top
  1. Asashiba, H., 10.1006/jabr.1997.6906, J. Algebra 191 (1997), 382-415. (1997) Zbl0871.16006MR1444505DOI10.1006/jabr.1997.6906
  2. Assem, I., Brüstle, T., Schiffler, R., Todorov, G., 10.1016/j.jalgebra.2005.12.002, J. Algebra 305 (2006), 548-561. (2006) Zbl1114.16010MR2264143DOI10.1016/j.jalgebra.2005.12.002
  3. Assem, I., Brüstle, T., Schiffler, R., Todorov, G., 10.1016/j.jpaa.2007.07.013, J. Pure Appl. Algebra 212 (2008), 884-901. (2008) Zbl1143.16015MR2363499DOI10.1016/j.jpaa.2007.07.013
  4. 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
  5. Enochs, E., Torrecillas, B., 10.1515/FORM.2011.021, Forum Math. 23 (2011), 611-624. (2011) Zbl1227.16002MR2805196DOI10.1515/FORM.2011.021
  6. Gao, N., Psaroudakis, C., 10.1007/s10468-016-9652-1, Algebr. Represent. Theory 20 (2017), 487-529. (2017) Zbl1382.16008MR3638357DOI10.1007/s10468-016-9652-1
  7. Green, E. L., 10.2140/pjm.1982.100.123, Pac. J. Math. 100 (1982), 123-138. (1982) Zbl0502.16016MR0661444DOI10.2140/pjm.1982.100.123
  8. Green, E. L., Psaroudakis, C., 10.1007/s10468-013-9457-4, Algebr. Represent. Theory 17 (2014), 1485-1525. (2014) Zbl1317.16003MR3260907DOI10.1007/s10468-013-9457-4
  9. Happel, D., Seidel, U., 10.1007/s10468-009-9169-y, Algebr. Represent. Theory 13 (2010), 693-704. (2010) Zbl1217.16015MR2736030DOI10.1007/s10468-009-9169-y
  10. Herscovich, E., Solotar, A., 10.1016/j.jalgebra.2007.05.014, J. Algebra 315 (2007), 852-873. (2007) Zbl1184.18013MR2351897DOI10.1016/j.jalgebra.2007.05.014
  11. Iversen, B., 10.1007/978-3-642-82783-9, Universitext, Springer, Berlin (1986). (1986) Zbl1272.55001MR0842190DOI10.1007/978-3-642-82783-9
  12. Ladkani, S., 10.1112/jlms/jds034, J. Lond. Math. Soc., II. Ser. 87 (2013), 157-176. (2013) Zbl1284.16008MR3022711DOI10.1112/jlms/jds034
  13. Li, L., 10.1080/00927872.2013.879157, Commun. Algebra 43 (2015), 1723-1741. (2015) Zbl1360.18003MR3316816DOI10.1080/00927872.2013.879157
  14. Li, L., 10.1080/00927872.2017.1327051, Commun. Algebra 46 (2018), 615-628. (2018) Zbl06875436MR3764883DOI10.1080/00927872.2017.1327051
  15. Miličić, D., Lectures on Derived Categories, Available at http://www.math.utah.edu/ {milicic/Eprints/dercat.pdf}. 
  16. Miyachi, J.-I., 10.1016/0022-4049(94)00145-6, J. Pure Appl. Algebra 105 (1995), 183-194. (1995) Zbl0846.16005MR1365875DOI10.1016/0022-4049(94)00145-6
  17. Rickard, J., 10.1016/0022-4049(89)90081-9, J. Pure Appl. Algebra 61 (1989), 303-317. (1989) Zbl0685.16016MR1027750DOI10.1016/0022-4049(89)90081-9
  18. Rickard, J., 10.1112/jlms/s2-39.3.436, J. Lond. Math. Soc., II. Ser. 39 (1989), 436-456. (1989) Zbl0642.16034MR1002456DOI10.1112/jlms/s2-39.3.436
  19. Rickard, J., 10.1112/jlms/s2-43.1.37, J. Lond. Math. Soc., II. Ser. 43 (1991), 37-48. (1991) Zbl0683.16030MR1099084DOI10.1112/jlms/s2-43.1.37
  20. Xi, C., 10.1007/s11464-016-0593-0, Front. Math. China 12 (2017), 1-18. (2017) Zbl1396.18010MR3569663DOI10.1007/s11464-016-0593-0
  21. Zhang, S., 10.1016/j.jalgebra.2010.02.002, J. Algebra 323 (2010), 2538-2546. (2010) Zbl1242.16015MR2602394DOI10.1016/j.jalgebra.2010.02.002

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.