skew group algebras
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2020 ◽  
Vol 108 (5-6) ◽  
pp. 769-774
Author(s):  
Hai Bui Xuan ◽  
Nam Cao Minh ◽  
Bien Mai Hoang

2020 ◽  
Vol 71 (3) ◽  
pp. 1009-1047
Author(s):  
Patrick Le Meur

Abstract Let $R$ be the skew group algebra of a finite group acting on the path algebra of a quiver. This article develops both theoretical and practical methods to do computations in the Morita-reduced algebra associated to $R$. Reiten and Riedtmann proved that there exists an idempotent $e$ of $R$ such that the algebra $eRe$ is both Morita equivalent to $R$ and isomorphic to the path algebra of some quiver, which was described by Demonet. This article gives explicit formulas for the decomposition of any element of $eRe$ as a linear combination of paths in the quiver described by Demonet. This is done by expressing appropriate compositions and pairings in a suitable monoidal category, which takes into account the representation theory of the finite group.


2019 ◽  
Vol 75 (1) ◽  
Author(s):  
Yonggang Hu ◽  
Hailou Yao

Author(s):  
M. H. Bien ◽  
M. Ramezan-Nassab

In this paper, we study some algebras [Formula: see text] whose unit groups [Formula: see text] or subnormal subgroups of [Formula: see text] are (generalized) Engel. For example, we show that any generalized Engel subnormal subgroup of the multiplicative group of division rings with uncountable centers is central. Some of algebraic structures of Engel subnormal subgroups of the unit groups of skew group algebras over locally finite or torsion groups are also investigated.


2019 ◽  
Vol 18 (10) ◽  
pp. 1950194
Author(s):  
Yueming Xiang ◽  
Lunqun Ouyang

Let [Formula: see text] be a finite dimensional algebra over a field [Formula: see text] and [Formula: see text] a subgroup of a finite group [Formula: see text]. In this paper, we consider the Gorenstein global dimensions and representation dimensions of the skew group algebras [Formula: see text] and [Formula: see text]. Under the assumption that [Formula: see text] is a separable extension over [Formula: see text], we show that [Formula: see text] and [Formula: see text] share the same Gorenstein global dimensions and representation dimensions. As an application, we give an affirmative answer for a conjecture raised in [Adjoint functors and representation dimensions, Acta Math. Sinica 22(2) (2006) 625–640]. Several known results are then obtained as corollaries.


2019 ◽  
Vol 526 ◽  
pp. 112-165
Author(s):  
Simone Giovannini ◽  
Andrea Pasquali

2019 ◽  
Vol 518 ◽  
pp. 211-236
Author(s):  
S. Fryer ◽  
T. Kanstrup ◽  
E. Kirkman ◽  
A.V. Shepler ◽  
S. Witherspoon

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