PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
1999 | 80 | 2 | 155-174
Tytuł artykułu

Symmetric Hochschild extension algebras

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
By an extension algebra of a finite-dimensional K-algebra A we mean a Hochschild extension algebra of A by the dual A-bimodule $Hom_K(A,K)$. We study the problem of when extension algebras of a K-algebra A are symmetric. (1) For an algebra A= KQ/I with an arbitrary finite quiver Q, we show a sufficient condition in terms of a 2-cocycle for an extension algebra to be symmetric. (2) Let L be a finite extension field of K. By using a given 2-cocycle of the K-algebra L, we construct a 2-cocycle of the K-algebra LQ for an arbitrary finite quiver Q without oriented cycles. Then we show a criterion on L for all those K-algebras LQ to have symmetric non-splittable extension algebras defined by the 2-cocycles.
Słowa kluczowe
Rocznik
Tom
80
Numer
2
Strony
155-174
Opis fizyczny
Daty
wydano
1999
otrzymano
1998-08-05
Twórcy
  • Institute of Mathematics, University of Tsukuba, 1-1-1 Tennodai, Tsukuba Ibaraki 305-0006, Japan
autor
  • Institute of Mathematics, University of Tsukuba, 1-1-1 Tennodai, Tsukuba Ibaraki 305-0006, Japan
  • Tokyo University of Agriculture and Technology, 3-5-8 Saiwaicho, Fuchu, Tokyo 183-0054, Japan
Bibliografia
  • [1] G. Azumaya and T. Nakayama, Algebra II (Ring Theory), Iwanami Shoten, Tokyo, 1958.
  • [2] H. Cartan and S. Eilenberg, Homological Algebra, Princeton Univ. Press, Princeton, N.J., 1956.
  • [3] Yu. A. Drozd and V. V. Kirichenko, Finite Dimensional Algebras, Springer, Berlin, 1994.
  • [4] S. Eilenberg, A. Rosenberg and D. Zelinsky, On the dimension of modules and algebras, VIII, Nagoya Math. J. 12 (1957), 71-93.
  • [5] K. Erdmann, O. Kerner and A. Skowroński, Self-injective algebras of wild tilted type, J. Pure Appl. Algebra, to appear.
  • [6] D. Happel, Hochschild cohomology of finite-dimensional algebras, in: Séminaire d'Algèbre P. Dubreil et M.-P. Malliavin 1987-88, Lecture Notes in Math. 1404, Springer, Berlin, 1989, 108-126.
  • [7] T. Nakayama, On Frobeniusean algebras, I, Ann. of Math. 40 (1939), 611-633.
  • [8] J. Rickard, Derived equivalences as derived functors, J. London Math. Soc. 43 (1991), 37-48.
  • [9] A. Skowroński and K. Yamagata, Socle deformations of self-injective algebras, Proc. London Math. Soc. 72 (1996), 545-566.
  • [10] A. Skowroński and K. Yamagata, Stable equivalence of selfinjective algebras of tilted type, Arch. Math. (Basel) 70 (1998), 341-350.
  • [11] K. Yamagata, Extensions over hereditary artinian rings with self-dualities, I, J. Algebra 73 (1981), 386-433.
  • [12] K. Yamagata, Representations of non-splittable extension algebras, J. Algebra 115 (1988), 32-45.
  • [13] K. Yamagata, Frobenius algebras, in: Handbook of Algebra, Vol. 1, Elsevier, 1996, 841-887.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-cmv80i2p155bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.