Journal of Mathematical Sciences

, Volume 188, Issue 5, pp 582–590 | Cite as

Cohomology of algebras of semidihedral type. VIII

Article

The present paper continues a cycle of papers of the author (same of them joint), in which the Yoneda algebras are calculated for several families of algebras of dihedral and semidihedral type (in K. Erdmam’s classification). In this paper, the Yaneda algebra is described in terms of quivers with relations for algebras of semidihedral type of the family SD(2\( \mathcal{B} \))2. Bibliography: 28 titles.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A. I. Generalov, “Cohomology of algebras of dihedral type. I,” Zap. Nauchn. Semin. POMI, 265, 139-162 (1999).Google Scholar
  2. 2.
    O. I. Balashov and A. I. Generalov, “Yoneda algebras of a class of dihedral algebras,” Vestn. Sankt Peterburg. Univ., Ser. 1, 3, No. 15, 3-10 (1999).Google Scholar
  3. 3.
    O. I. Balashov and A. I. Generalov, “Cohomology of algebras of dihedral type. II,” Algebra Analiz, 13, No. 1, 3-25 (2001).MathSciNetGoogle Scholar
  4. 4.
    A. I. Generalov, “Cohomology of algebras of semidihedral type. I,” Algebra Analiz, 13, No. 4, 54-85 (2001).MathSciNetGoogle Scholar
  5. 5.
    N. V. Kosmatov, “Cohomology of algebras of dihedral type: automatic calculation,” in: International Algebraic Conference dedicated to the memory of Z. I. Borevich (2002), pp. 115-116.Google Scholar
  6. 6.
    M. A. Antipov and A. I. Generalov, “Cohomology of algebras of semidihedral type. II,” Zap. Nauchn. Semin. POMI, 289. 9-36 (2002).Google Scholar
  7. 7.
    A. I. Generalov, “Cohomology of algebras of dihedral type. IV: the family D(2\( \mathcal{B} \)),” Zap. Nauchn. Semin. POMI, 289, 76-89 (2002).Google Scholar
  8. 8.
    A. I. Generalov and E. A. Osiuk, “Cohomology of algebras of dihedral type. III: the family D(2\( \mathcal{A} \)),” Zap. Nauchn. Semin. POMI, 289, 113-133 (2002).Google Scholar
  9. 9.
    A. I. Generalov, “Cohomology of algebras of semidihedral type. III: the family SD(3\( \mathcal{K} \)),” Zap. Nauchn. Semin. POMI, 305, 84-100 (2003).Google Scholar
  10. 10.
    A. I. Generalov and N. V. Kosmatov, “Computation of the Yoneda algebras of dihedral type,” Zap. Nauchn. Semin. POMI, 305, 101-120 (2003).Google Scholar
  11. 11.
    A. I. Generalov. “Cohomology of algebras of semidihedral type. IV.” Zap. Nauchn. Semin. POMI, 319, 81-116 (2004).Google Scholar
  12. 12.
    A. I. Generalov and N. V. Kosmatov, “Projective resolutions and Yoneda algebras for algebras of dihedral type: the family D(3\( \mathcal{Q} \)),” Fundam. Prikl. Matem., 10, 65-89, No. 4 (2004).MATHGoogle Scholar
  13. 13.
    A. I. Generalov, “Cohomology of algebras of semidihedral type. V,” Zap. Nauchn. Semin. POMI, 330, 131-154 (2006).MATHGoogle Scholar
  14. 14.
    A. I. Generalov, “Cohomology of algebras of semidihedral type. VI,” Zap. Nauchn. Semin. POMI, 343, 183-198 (2007).MathSciNetGoogle Scholar
  15. 15.
    A. I. Generalov, “Cohomology of algebras of semidihedral type. VII. Local algebras,” Zap. Nauchn. Semin. POMI, 365, 130-142 (2009).MathSciNetGoogle Scholar
  16. 16.
    K. Erdmann. “Blocks of tame representation type and related algebras.” Lect. Notes Math., 1428 (1990).Google Scholar
  17. 17.
    D. J. Benson and J. F. Carlson, “Diagrammatic methods for modular representations and cohomology,” Commun. Algebra, 15, No. 1/2, 53-121 (1987).MathSciNetMATHCrossRefGoogle Scholar
  18. 18.
    A. I. Generalov, “Hochschild cohomology of algebras of dihedral type. I: the family D(3\( \mathcal{K} \)) in characteristic 2,” Algebra Analiz, 16, No. 6, 53-122 (2004).MathSciNetGoogle Scholar
  19. 19.
    A. I. Generalov, “Hochschild cohomology of algebras of quaternion type. I: generalized quaternion groups,” Algebra Analiz, 18, No. 1, 55-107 (2006).MathSciNetGoogle Scholar
  20. 20.
    A. I. Generalov and N. Yu. Kossovskaya, “Hochschild cohomology of Liu-Schulz algebras,” Algebra Analiz, 18, No. 4, 39-82 (2006).Google Scholar
  21. 21.
    A. I. Generalov, A. A. Ivanov, and S. O. Ivanov, “Hochschild cohomology of algebras of quaternion type. II. The family Q(2\( \mathcal{B} \))l in characteristic 2,” Zap. Nauchn. Semin. POMI, 349, 53-134 (2007).Google Scholar
  22. 22.
    A. I. Generalov, “Hochschild cohomology of the integral group algebra of the dihedral group. I. Even case,” Algebra Analiz, 19, No. 5, 70-123 (2007).MathSciNetGoogle Scholar
  23. 23.
    A. I. Generalov, “Hochschild cohomology of algebras of quaternion type. III. Algebras with a small parameter,” Zap. Nauchn. Semin. POMI, 356, 46-84 (2008).Google Scholar
  24. 24.
    A. I. Generalov, “Hochschild cohomology of algebras of semidihedral type. I. Group algebras of semidihedral groups,” Algebra Analiz, 21, No. 2, 1-51 (2009).MathSciNetGoogle Scholar
  25. 25.
    A. I. Generalov, “Hochschild cohomology of algebras of dihedral type. II. Local algebras,” Zap. Nauchn. Semin. POMI, 375, 92-129 (2010).MathSciNetGoogle Scholar
  26. 26.
    A. I. Generalov, “Hochschild cohomology for algebras of dihedral type. III. Local algebras in characteristic 2,” Vestn. Sankt Peterburg. Univ., Ser. 1, 1, 28-38 (2010).Google Scholar
  27. 27.
    A. I. Geheralev, “Hochschild cohomology of algebras of semidihedral type. II. Local algebras,” Zap. Nauchn. Semin. POMI, 386, 144—202 (2011).Google Scholar
  28. 28.
    A. I. Generalov, “Hochschild cohomology of the integral group algebra of the semidihedral group," Zap. Nauchn. Semin. POMI, 388, 119-151 (2011).Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.St.Petersburg State UniversitySt. PetersburgRussia

Personalised recommendations