Abstract
AbstractWe study the combinatorics of an analogue of Green’s $${\mathcal {J}}$$
J
-relation (a.k.a. the two-sided relation) for the bicategory of finite-dimensional bimodules over finite-dimensional associative algebras over a fixed field. In particular, we provide a number of exameples for both $${\mathcal {J}}$$
J
-equivalent and inequivalent but $${\mathcal {J}}$$
J
-comparabe algebras.
Publisher
Springer Science and Business Media LLC
Reference39 articles.
1. Anderson, F. W., Fuller, K. R.: Rings and categories of modules. Graduate texts in mathematics 13, Second edition. Springer, New York (1998)
2. Broué, M.: Equivalences of blocks of group algebras. V. Dlab and L. Scott eds. Proc. of the NATO Advanced Research Workshop on Representation of Algebras and Related Topics, Kluwer Academic Publishers, Dordrecht, 1–26 (1991)
3. Butler, M.C.R., Ringel, C.M.: Auslander–Reiten sequences with few middle terms and applications to string algebras. Commun. Algebra 15(1–2), 145–179 (1987)
4. Chan, A., Mazorchuk, V.: Diagrams and discrete extensions for finitary $$2$$-representations. Math. Proc. Camb. Philos. Soc. 166, 325–352 (2019)
5. Chen, X., Sun, L.: Singular equivalences of Morita type (Preprint)