scholarly journals Homological dimensions of smooth crossed products

2021 ◽  
Vol 12 (3) ◽  
Author(s):  
Petr Kosenko
Keyword(s):  
Crossed Products ◽  
Homological Dimensions

scholarly journals HOMOLOGICAL DIMENSIONS OF CROSSED PRODUCTS

2016 ◽  
Vol 59 (2) ◽  
pp. 401-420 ◽  
Author(s):  
LIPING LI
Keyword(s):  
Global Dimension ◽  
Derived Categories ◽  
Group Algebras ◽  
Group Rings ◽  
Crossed Products ◽  
Finitistic Dimension ◽  
Homological Dimensions ◽  
Complete Set ◽  
A Finite Group ◽  
Skew Group Algebras

AbstractIn this paper, we consider several homological dimensions of crossed products AασG, where A is a left Noetherian ring and G is a finite group. We revisit the induction and restriction functors in derived categories, generalizing a few classical results for separable extensions. The global dimension and finitistic dimension of AσαG are classified: global dimension of AσαG is either infinity or equal to that of A, and finitistic dimension of AσαG coincides with that of A. A criterion for skew group rings to have finite global dimensions is deduced. Under the hypothesis that A is a semiprimary algebra containing a complete set of primitive orthogonal idempotents closed under the action of a Sylow p-subgroup S ≤ G, we show that A and AασG share the same homological dimensions under extra assumptions, extending the main results in (Li, Representations of modular skew group algebras, Trans. Amer. Math. Soc.367(9) (2015), 6293–6314, Li, Finitistic dimensions and picewise hereditary property of skew group algebras, to Glasgow Math. J.57(3) (2015), 509–517).

scholarly journals Dominant and global dimension of blocks of quantised Schur algebras

2021 ◽  
Author(s):  
Ming Fang ◽  
Wei Hu ◽  
Steffen Koenig
Keyword(s):  
Hecke Algebras ◽  
Symmetric Groups ◽  
Global Dimension ◽  
Group Algebras ◽  
Dominant Dimension ◽  
Schur Algebras ◽  
Homological Dimensions ◽  
Weyl Duality

AbstractGroup algebras of symmetric groups and their Hecke algebras are in Schur-Weyl duality with classical and quantised Schur algebras, respectively. Two homological dimensions, the dominant dimension and the global dimension, of the indecomposable summands (blocks) of these Schur algebras S(n, r) and $$S_q(n,r)$$ S q ( n , r ) with $$n \geqslant r$$ n ⩾ r are determined explicitly, using a result on derived invariance in Fang, Hu and Koenig (J Reine Angew Math 770:59–85, 2021).

scholarly journals Discrete Product Systems and Twisted Crossed Products by Semigroups

1998 ◽  
Vol 155 (1) ◽  
pp. 171-204 ◽  
Author(s):  
Neal J. Fowler ◽  
Iain Raeburn
Keyword(s):  
Crossed Products ◽  
Product Systems

Central sequences in crossed products of full factors

1982 ◽  
Vol 49 (1) ◽  
pp. 29-33 ◽  
Author(s):  
V. F. R. Jones
Keyword(s):  
Crossed Products ◽  
Central Sequences

scholarly journals Generalized crossed products and Azumaya algebras

1991 ◽  
Vol 136 (2) ◽  
pp. 275-289
Author(s):  
K.-H Ulbrich
Keyword(s):  
Crossed Products ◽  
Azumaya Algebras

scholarly journals The Dixmier-Douady class of groupoid crossed products

2004 ◽  
Vol 76 (2) ◽  
pp. 223-234 ◽  
Author(s):  
Paul S. Muhly ◽  
Dana P. Williams
Keyword(s):  
Crossed Product ◽  
Crossed Products ◽  
Continuous Trace

AbstractWe give a formula for the Dixmier-Douady class of a continuous-trace groupoid crossed product that arises from an action of a locally trivial, proper, principal groupoid on a bundle of elementary C*-algebras that satisfies Fell's condition.

scholarly journals On deformations of crossed products

2007 ◽  
Vol 210 (1) ◽  
pp. 81-91
Author(s):  
Eli Aljadeff ◽  
Yuval Ginosar ◽  
Andy R. Magid
Keyword(s):  
Crossed Products

scholarly journals The Jacobson Radical for Analytic Crossed Products

2001 ◽  
Vol 187 (1) ◽  
pp. 129-145 ◽  
Author(s):  
Allan P Donsig ◽  
Aristides Katavolos ◽  
Antonios Manoussos
Keyword(s):  
Jacobson Radical ◽  
Crossed Products

Homological Dimensions Relative to Special Subcategories

2021 ◽  
Vol 28 (01) ◽  
pp. 131-142
Author(s):  
Weiling Song ◽  
Tiwei Zhao ◽  
Zhaoyong Huang
Keyword(s):  
Abelian Category ◽  
Projective Dimension ◽  
Homological Dimensions ◽  
Category Of Modules ◽  
The Right

Let [Formula: see text] be an abelian category, [Formula: see text] an additive, full and self-orthogonal subcategory of [Formula: see text] closed under direct summands, [Formula: see text] the right Gorenstein subcategory of [Formula: see text] relative to [Formula: see text], and [Formula: see text] the left orthogonal class of [Formula: see text]. For an object [Formula: see text] in [Formula: see text], we prove that if [Formula: see text] is in the right 1-orthogonal class of [Formula: see text], then the [Formula: see text]-projective and [Formula: see text]-projective dimensions of [Formula: see text] are identical; if the [Formula: see text]-projective dimension of [Formula: see text] is finite, then the [Formula: see text]-projective and [Formula: see text]-projective dimensions of [Formula: see text] are identical. We also prove that the supremum of the [Formula: see text]-projective dimensions of objects with finite [Formula: see text]-projective dimension and that of the [Formula: see text]-projective dimensions of objects with finite [Formula: see text]-projective dimension coincide. Then we apply these results to the category of modules.

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