Geodesic
Derived equivalence of symmetric special biserial algebras
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 15, Tome 343 (2007), pp. 5-32 
M. A. Antipov. Derived equivalence of symmetric special biserial algebras. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 15, Tome 343 (2007), pp. 5-32. http://geodesic.mathdoc.fr/item/ZNSL_2007_343_a0/
@article{ZNSL_2007_343_a0,
     author = {M. A. Antipov},
     title = {Derived equivalence of symmetric special biserial algebras},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {5--32},
     year = {2007},
     volume = {343},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2007_343_a0/}
}
TY  - JOUR
AU  - M. A. Antipov
TI  - Derived equivalence of symmetric special biserial algebras
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2007
SP  - 5
EP  - 32
VL  - 343
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2007_343_a0/
LA  - ru
ID  - ZNSL_2007_343_a0
ER  - 
%0 Journal Article
%A M. A. Antipov
%T Derived equivalence of symmetric special biserial algebras
%J Zapiski Nauchnykh Seminarov POMI
%D 2007
%P 5-32
%V 343
%U http://geodesic.mathdoc.fr/item/ZNSL_2007_343_a0/
%G ru
%F ZNSL_2007_343_a0

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

We introduce Brauer complex of symmetric special biserial algebra, and reformulate in terms of Brauer complex the presently known invariants of stable and derived equivalence of symmetric special biserial algebra. In particular, the genus of Brauer complex turns out to be invariant under derived equivalence. We study transformations of Brauer complexes which preserve class of derived equivalence. As a consequence, symmetric special biserial algebra with Brauer complex of genus 0 are classified.

[1] M. A. Antipov, A. I. Generalov, “Konechnaya porozhdennost algebry Ionedy simmetricheskikh spetsialnykh biryadnykh algebr”, Algebra i analiz, 17:3 (2005), 1–23 | MR | Zbl

[2] M. A. Antipov, “Invarianty stabilnoi ekvivalentnosti simmetricheskikh spetsialnykh biryadnykh algebr”, Zap. nauchn. semin. POMI, 330, 2006, 5–28 | MR | Zbl

[3] J. Rickard, “Derived categories and stable equivalence”, J. Pure Appl. Algebra, 61 (1989), 303–317 | DOI | MR | Zbl

[4] Th. Holm, “Derived equivalence classification of algebras of dihedral, semidihedral, and quaternion type”, J. Algebra, 211:1 (1999), 159–205 | DOI | MR | Zbl

[5] J. Rickard, “Morita theory for derived categories”, J. London Math. Soc., 39 (1989), 436–456 | DOI | MR | Zbl

[6] S. K. Lando, A. K. Zvonkin, Graphs on Surfaces and Their Applications, Springer-Verlag, Berlin et al., 2004 | MR | Zbl

[7] Z. Pogorzaly, “On a construction of algebras stably equivalent to selfinjective special biserial algebras”, Ann. Sci. Math. Quebec, 17:1 (1993), 65–97 | MR | Zbl