Geodesic
Structure of the stable Grothendieck group of a symmetric SB-algebra
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 18, Tome 365 (2009), pp. 29-46 Cet article a éte moissonné depuis la source Math-Net.Ru

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We determine the structure of the stable Grothendieck group of an arbitrary symmetric special biserial algebra in terms of multiplicities of $A$-cycles. Bibl. – 2 titles. 
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     author = {M. A. Antipov},
     title = {Structure of the stable {Grothendieck} group of a~symmetric {SB-algebra}},
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M. A. Antipov. Structure of the stable Grothendieck group of a symmetric SB-algebra. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 18, Tome 365 (2009), pp. 29-46. http://geodesic.mathdoc.fr/item/ZNSL_2009_365_a1/

[1] M. A. Antipov, “Gruppa Grotendika stabilnoi kategorii simmetricheskoi spetsialnoi biryadnoi algebry”, Zap. nauchn. semin. POMI, 321, 2005, 5–12 | MR | Zbl

[2] H. Tachikawa, T. Vakamatsu, “Cartan matrices and Grothendieck groups of stable categories”, J. Algebra, 144:2 (1991), 390–398 | DOI | MR | Zbl