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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     author = {M. A. Antipov},
     title = {Derived equivalence of symmetric special biserial algebras},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2007_343_a0/}
}
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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/

[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