|
A new invariant of stable equivalences of Morita type
Author(s):
Zygmunt
Pogorzaly
Journal:
Proc. Amer. Math. Soc.
131
(2003),
343-349.
MSC (2000):
Primary 16D50;
Secondary 16G20
Posted:
June 5, 2002
Retrieve article in:
PDF DVI PostScript
Abstract |
References |
Similar articles |
Additional information
Abstract:
It was proved in an earlier paper by the author that the Hochschild cohomology algebras of self-injective algebras are invariant under stable equivalences of Morita type. In this note we show that the orbit algebra of a self-injective algebra  (considered as an  - -bimodule) is also invariant under stable equivalences of Morita type, where the orbit algebra is the algebra of all stable  - -bimodule morphisms from the non-negative Auslander-Reiten translations of  to  .
References:
-
- [1]
- H. Asashiba, A covering technique for derived equivalence, J. Algebra 191(1997), 382-415. MR 98b:16009
- [2]
- H. Asashiba, The derived equivalence classification of representation-finite selfinjective algebras, J. Algebra 214(1999), 182-221. MR 2000g:16019
- [3]
- M. Auslander, I. Reiten and S. Smalo, Representation Theory of Artin Algebras, Cambridge Studies in Advanced Math. Vol. 36, Cambridge Univ. Press (Cambridge, 1995). MR 96e:16015
- [4]
- M. Broué, Equivalences of Blocks of Group Algebras, in: V. Dlab and L.L. Scott (eds.) Finite Dimensional Algebras and Related Topics, NATO ASI Series C Vol. 424, Kluwer Academic Press (Dodrecht, 1992), 1-26. MR 97c:20004
- [5]
- P. Gabriel, Auslander-Reiten sequences and representation-finite algebras, Lecture Notes in Math. 831(Springer-Verlag, Berlin, 1980), 1-71. MR 82i:16030
- [6]
- D. Happel, Triangulated categories in the representation theory of finite-dimensional algebras, London Math. Soc. Lecture Notes 119, Cambridge Univ. Press (Cambridge, 1988). MR 89e:16035
- [7]
- D. Happel, Hochschild cohomology of finite-dimensional algebras, in: Seminair d'Algebre P. Dubriel et M-P.Maliavin, Lecture Notes in Math. 1404(Springer-Verlag, Berlin, 1989), 108-126. MR 91b:16012
- [8]
- A. Heller, The loop-space functor in homological algebra, Trans. Amer. Math. Soc. 96(1960), 382-394. MR 22:6840
- [9]
- O. Kerner, Minimal approximations, orbital elementary modules, and orbit algebras of regular modules, J. Algebra 217(1999), 528-554. MR 2000e:16018
- [10]
- H. Lenzing, Wild Canonical Alebras and Rings of Automorphic Forms, in: V. Dlab and L.L. Scott (eds.) Finite Dimensional Algebras and Related Topics, NATO ASI Series C Vol. 424, Kluwer Academic Press (Dodrecht, 1992), 191-212. MR 95m:16008
- [11]
- M. Linckelmann, Stable equivalences of Morita type for self-injective algebras and
 -groups, Math. Z. 223(1996), 87-100. MR 97j:20011 - [12]
- S. Mac Lane, Homology, (Springer-Verlag, Berlin, 1963). MR 28:122
- [13]
- Z. Pogorza
 y, Invariance of Hochschild cohomology algebras under stable equivalences of Morita type, J. Math. Soc. Japan 53(2001), 913-918. - [14]
- Z. Pogorza
 y, Left-right projective bimodules and stable equivalences of Morita type, Colloq. Math. Vol.88 (2) (2001), 243-255. - [15]
- J. Rickard, Derived equivalences as derived functors, J. London Math. Soc. (2) 43(1991), 37-48. MR 92b:16043
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
16D50,
16G20
Retrieve articles in all Journals with MSC
(2000):
16D50,
16G20
Additional Information:
Zygmunt
Pogorzaly
Affiliation:
Faculty of Mathematics and Computer Science, Nicholas Copernicus University, Chopina 12/18, 87-100 Torun, Poland
Email:
zypo@mat.uni.torun.pl
DOI:
10.1090/S0002-9939-02-06553-X
PII:
S 0002-9939(02)06553-X
Received by editor(s):
May 2, 2001
Received by editor(s) in revised form:
September 6, 2001
Posted:
June 5, 2002
Dedicated:
Dedicated to Professor Idun Reiten on the occasion of her sixtieth birthday
Communicated by:
Martin Lorenz
Copyright of article:
Copyright
2002,
American Mathematical Society
|
Comments: webmaster@ams.org