Stable equivalences of morita type for self-injective algebras andp-groups

1996 ◽  
Vol 223 (1) ◽  
pp. 87-100 ◽  
Author(s):  
Markus Linckelmann
Keyword(s):  
Stable Equivalences ◽  
Morita Type

scholarly journals Stable equivalences of Morita type do not preserve tensor products and trivial extensions of algebras

2017 ◽  
Vol 145 (5) ◽  
pp. 1881-1890 ◽  
Author(s):  
Yuming Liu ◽  
Guodong Zhou ◽  
Alexander Zimmermann
Keyword(s):  
Tensor Products ◽  
Stable Equivalences ◽  
Morita Type

scholarly journals Integrable Derivations and Stable Equivalences of Morita Type

2018 ◽  
Vol 61 (2) ◽  
pp. 343-362 ◽  
Author(s):  
Markus Linckelmann
Keyword(s):  
Hochschild Cohomology ◽  
Block Theory ◽  
Discrete Valuation Rings ◽  
Symmetric Algebras ◽  
Valuation Rings ◽  
Transfer Maps ◽  
Stable Equivalences ◽  
Morita Type

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.

Stable equivalences of Morita type and stable Hochschild cohomology rings

2010 ◽  
Vol 94 (6) ◽  
pp. 511-518 ◽  
Author(s):  
Shengyong Pan ◽  
Guodong Zhou
Keyword(s):  
Hochschild Cohomology ◽  
Cohomology Rings ◽  
Stable Equivalences ◽  
Morita Type

scholarly journals Classifying tame blocks and related algebras up to stable equivalences of Morita type

2011 ◽  
Vol 215 (12) ◽  
pp. 2969-2986 ◽  
Author(s):  
Guodong Zhou ◽  
Alexander Zimmermann
Keyword(s):  
Stable Equivalences ◽  
Morita Type

Rigidity dimension of algebras

2019 ◽  
pp. 1-27
Author(s):  
HONGXING CHEN ◽  
MING FANG ◽  
OTTO KERNER ◽  
STEFFEN KOENIG ◽  
KUNIO YAMAGATA
Keyword(s):  
Hochschild Cohomology ◽  
Global Dimension ◽  
Homological Dimension ◽  
Dominant Dimension ◽  
Finite Global Dimension ◽  
Derived Equivalences ◽  
Finite Dimensional ◽  
Stable Equivalences ◽  
Morita Type

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.

scholarly journals A note on stable equivalences of Morita type

2007 ◽  
Vol 208 (2) ◽  
pp. 421-433 ◽  
Author(s):  
Alex S. Dugas ◽  
Roberto Martínez-Villa
Keyword(s):  
Stable Equivalences ◽  
Morita Type

Summands of Stable Equivalences of Morita Type

2008 ◽  
Vol 36 (10) ◽  
pp. 3778-3782 ◽  
Author(s):  
Yuming Liu
Keyword(s):  
Stable Equivalences ◽  
Morita Type

scholarly journals Inductions and restrictions for stable equivalences of Morita type

2012 ◽  
Vol 216 (3) ◽  
pp. 643-661 ◽  
Author(s):  
Hongxing Chen ◽  
Shengyong Pan ◽  
Changchang Xi
Keyword(s):  
Stable Equivalences ◽  
Morita Type
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