Geodesic
Projective resolutions and Yoneda algebras for algebras of dihedral type: the family $D(3\mathcal Q)$
Fundamentalʹnaâ i prikladnaâ matematika, Tome 10 (2004) no. 4, pp. 65-89.

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This paper provides a method for the computation of Yoneda algebras for algebras of dihedral type. The Yoneda algebras for one infinite family of algebras of dihedral type (the family $D(3\mathcal Q)$ in K. Erdmann's notation) are computed. The minimal projective resolutions of simple modules were calculated by an original computer program implemented by one of the authors in C++ language. The algorithm of the program is based on a diagrammatic method presented in this paper and inspired by that of D. Benson and J. Carlson. 
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A. I. Generalov; N. V. Kosmatov. Projective resolutions and Yoneda algebras for algebras of dihedral type: the family $D(3\mathcal Q)$. Fundamentalʹnaâ i prikladnaâ matematika, Tome 10 (2004) no. 4, pp. 65-89. http://geodesic.mathdoc.fr/item/FPM_2004_10_4_a5/

[1] Antipov M. A., Generalov A. I., “Kogomologii algebr poludiedralnogo tipa, II”, Zap. nauch. sem. Sankt-Peterburg. otd-niya Mat. in-ta im. V. A. Steklova RAN, 289, 2002, 9–36 | Zbl

[2] Balashov O. I., Generalov A. I., “Algebry Ionedy dlya odnogo klassa diedralnykh algebr”, Vestn. S.-Peterb. un-ta. Ser. 1, 3:15 (1999), 3–10 | MR | Zbl

[3] Balashov O. I., Generalov A. I., “Kogomologii algebr diedralnogo tipa, II”, Algebra i analiz, 13:1 (2001), 3–25 | MR

[4] Generalov A. I., “Kogomologii algebr diedralnogo tipa, I”, Zap. nauch. sem. Sankt-Peterburg. otd-niya Mat. in-ta im. V. A. Steklova RAN, 265, 1999, 139–162 | MR

[5] Generalov A. I., “Kogomologii algebr poludiedralnogo tipa, I”, Algebra i analiz, 13:4 (2001), 54–85 | MR | Zbl

[6] Generalov A. I., Osiyuk E. A., “Kogomologii algebr diedralnogo tipa, III: seriya $D(2\mathcal A)$”, Zap. nauch. sem. Sankt-Peterburg. otd-niya Mat. in-ta im. V. A. Steklova RAN, 289, 2002, 113–133 | MR | Zbl

[7] Generalov A. I., “Kogomologii algebr diedralnogo tipa, IV: seriya $D(2\mathcal B)$”, Zap. nauch. sem. Sankt-Peterburg. otd-niya Mat. in-ta im. V. A. Steklova RAN, 289, 2002, 76–89 | MR | Zbl

[8] Generalov A. I., “Kogomologii algebr poludiedralnogo tipa, III: seriya $SD(3\mathcal K)$”, Zap. nauch. sem. Sankt-Peterburg. otd-niya Mat. in-ta im. V. A. Steklova RAN, 305, 2003, 84–100 | MR

[9] Alperin J. L., “Diagrams for modules”, J. Pure Appl. Algebra, 16:2 (1980), 111–119 | DOI | MR | Zbl

[10] Benson D. J., Representations and Cohomology, I: Basic Representation Theory of Finite Groups and Associative Algebras, Cambridge Univ. Press, Cambridge, 1991 | MR

[11] Benson D. J., Carlson J. F., “Diagrammatic methods for modular representations and cohomology”, Comm. Algebra, 15:1–2 (1987), 53–121 | DOI | MR | Zbl

[12] Erdmann K., Blocks of Tame Representation Type and Related Algebras, Lecture Notes in Math., 1428, Springer, Berlin, 1990 | MR | Zbl

[13] Fuller K. R., “Algebras from diagrams”, J. Pure Appl. Algebra, 48:1–2 (1987), 23–37 | DOI | MR | Zbl

[14] Generalov A. I., Kosmatov N. V., “Computation of the Yoneda algebras of dihedral type”, Zap. nauch. sem. Sankt-Peterburg. otd-niya Mat. in-ta im. V. A. Steklova RAN, 305, 2003, 101–120 | MR

[15] Kosmatov N., Resolut, , 2003 http://www.lifc.univ-fcomte.fr/