TILTED ALGEBRAS AND CROSSED PRODUCTS*
Glasgow mathematical journal, Tome 58 (2016) no. 3, pp. 559-571

Voir la notice de l'article provenant de la source Cambridge University Press

We consider an artin algebra A and its crossed product algebra A α#σ G, where G is a finite group with its order invertible in A. Then, we prove that A is a tilted algebra if and only if so is A α#σ G.
LIN, YANAN; ZHOU, ZHENQIANG. TILTED ALGEBRAS AND CROSSED PRODUCTS*. Glasgow mathematical journal, Tome 58 (2016) no. 3, pp. 559-571. doi: 10.1017/S0017089515000336
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[1] 1. Assem, I., Simson, D. and Skowroński, A., Elements of the representation theory of associative algebras, Vol. 1, London Mathematical Society Student Texts, vol. 65 (Cambridge University Press, Cambridge, 2006). Google Scholar

[2] 2. Auslander, M., Reiten, I. and Smalø, S., Representation theory of artin algebras, Cambridge Stud. Adv. Math., vol. 36 (Cambridge University Press, Cambridge, 1995). Google Scholar

[3] 3. Barannyk, L. F., On uniserial twisted group algebras of finite p-groups over a field of characteristic p , J. Algebra 403 (2014), 300–312. Google Scholar

[4] 4. Barannyk, L. F. and Klein, D., On twisted group algebras of OTP representation type, Colloq. Math. 127 (2012), 213–232. Google Scholar

[5] 5. Colby, R. and Fuller, K., Equivalence and duality for module categories, Cambridge Tracts in Math., vol. 161 (Cambridge University Press, Cambridge, 2004). Google Scholar

[6] 6. Curtis, C. W. and Reiner, I., Methods of representation theory with applications to finite groups and orders, vol. 1 (John Wiley and Sons, New York, 1981). Google Scholar

[7] 7. Happel, D. and Ringel, C., Tilted algebras, Trans. Amer. Math. Soc. 274 (1982), 339–443. Google Scholar

[8] 8. Liu, S., Tilted algebras and generalized standard Auslander-Reiten components, Archiv Math. 61 (1993), 12–19. Google Scholar

[9] 9. Liu, S., The connected components of the Auslander-Reiten quiver of a tilted algebras, J. Algebra 161 (1993), 505–523. Google Scholar | DOI

[10] 10. Nastasescu, C. and Oystaeyen, F. V., Methods of graded rings, Lecture Notes in Mathematics, vol. 1836 (Springer-Verlag, Berlin, 2003). Google Scholar

[11] 11. Pierce, R. S., Associative algebras, Graduate Texts in Mathematics, vol. 88 (Springer-Verlag, New York, 1982). Google Scholar

[12] 12. Reiten, I. and Riedtmann, C., Skew group algebras in the representation theory of artin algebras, J. Algebra 92 (1985), 224–282. Google Scholar

[13] 13. Ringel, C., Some remarks concerning tilting modules and tilted algebras. Origin. Relevance. Future. in Handbook of tilting theory, LMS Lecture Note Ser., vol. 332 (Cambridge University Press, Cambridge, 2007), 49–104. Google Scholar

[14] 14. Simson, D. and Skowroński, A., Elements of the representation theory of associative algebras, Vol. 2, London Mathematical Society Student Texts, vol. 71 (Cambridge University Press, Cambridge, 2007). Google Scholar

[15] 15. Skowroński, A., Generalized standard Auslander-Reiten components without oriented cycles, Osaka J. Math. 30 (1993), 515–527. Google Scholar

[16] 16. Skowroński, A., Generalized standard Auslander-Reiten components, J. Math. Soc. Japan 46 (1994), 517–543. Google Scholar

[17] 17. Theohari-Apostolidi, Th. and Tompoulidou, A., On local weak crossed product orders, Colloq. Math. 135 (2014), 53–68. Google Scholar

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