stable equivalences
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Author(s):  
HONGXING CHEN ◽  
MING FANG ◽  
OTTO KERNER ◽  
STEFFEN KOENIG ◽  
KUNIO YAMAGATA

Abstract A new homological dimension, called rigidity dimension, is introduced to measure the quality of resolutions of finite dimensional algebras (especially of infinite global dimension) by algebras of finite global dimension and big dominant dimension. Upper bounds of the dimension are established in terms of extensions and of Hochschild cohomology, and finiteness in general is derived from homological conjectures. In particular, the rigidity dimension of a non-semisimple group algebra is finite and bounded by the order of the group. Then invariance under stable equivalences is shown to hold, with some exceptions when there are nodes in case of additive equivalences, and without exceptions in case of triangulated equivalences. Stable equivalences of Morita type and derived equivalences, both between self-injective algebras, are shown to preserve rigidity dimension as well.



2018 ◽  
Vol 222 (9) ◽  
pp. 2703-2717 ◽  
Author(s):  
Lizhong Wang ◽  
Jiping Zhang


2018 ◽  
Vol 61 (2) ◽  
pp. 343-362 ◽  
Author(s):  
Markus Linckelmann

AbstractUsing that integrable derivations of symmetric algebras can be interpreted in terms of Bockstein homomorphisms in Hochschild cohomology, we show that integrable derivations are invariant under the transfer maps in Hochschild cohomology of symmetric algebras induced by stable equivalences of Morita type. With applications in block theory in mind, we allow complete discrete valuation rings of unequal characteristic.



2018 ◽  
Vol 34 (1) ◽  
pp. 59-110 ◽  
Author(s):  
Wei Hu ◽  
Changchang Xi




2017 ◽  
Vol 288 (1-2) ◽  
pp. 531-539
Author(s):  
Zygmunt Pogorzały


2017 ◽  
Vol 145 (5) ◽  
pp. 1881-1890 ◽  
Author(s):  
Yuming Liu ◽  
Guodong Zhou ◽  
Alexander Zimmermann


2017 ◽  
Vol 469 ◽  
pp. 288-301
Author(s):  
Lleonard Rubio y Degrassi
Keyword(s):  


2015 ◽  
Vol 434 ◽  
pp. 27-45 ◽  
Author(s):  
Markus Linckelmann
Keyword(s):  


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