scholarly journals On the representation dimension of skew group algebras, wreath products and blocks of Hecke algebras

2013 ◽  
Vol 46 (1) ◽  
pp. 43-50
Author(s):  
Petter Andreas Bergh ◽  
Will Turner
Keyword(s):  
Hecke Algebras ◽  
Wreath Products ◽  
Group Algebras ◽  
Representation Dimension ◽  
Skew Group Algebras

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 Color Lie rings and PBW deformations of skew group algebras

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

scholarly journals Finite generation of the cohomology of some skew group algebras

2014 ◽  
Vol 8 (7) ◽  
pp. 1647-1657 ◽  
Author(s):  
Van Nguyen ◽  
Sarah Witherspoon
Keyword(s):  
Group Algebras ◽  
Finite Generation ◽  
Skew Group Algebras

Some algebraic algebras with Engel unit groups

2019 ◽  
pp. 2150010
Author(s):  
M. H. Bien ◽  
M. Ramezan-Nassab
Keyword(s):  
Multiplicative Group ◽  
Subnormal Subgroup ◽  
Group Algebras ◽  
Algebraic Structures ◽  
Locally Finite ◽  
Division Rings ◽  
Torsion Groups ◽  
Skew Group Algebras ◽  
Subnormal Subgroups

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.

scholarly journals ON THE MORITA REDUCED VERSIONS OF SKEW GROUP ALGEBRAS OF PATH ALGEBRAS

2020 ◽  
Vol 71 (3) ◽  
pp. 1009-1047
Author(s):  
Patrick Le Meur
Keyword(s):  
Finite Group ◽  
Monoidal Category ◽  
Path Algebra ◽  
Group Algebras ◽  
Explicit Formulas ◽  
Morita Equivalent ◽  
Path Algebras ◽  
A Finite Group ◽  
Skew Group Algebras ◽  
Skew Group Algebra

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.

G-Invariant Recollements and Skew Group Algebras

2019 ◽  
Vol 75 (1) ◽  
Author(s):  
Yonggang Hu ◽  
Hailou Yao
Keyword(s):  
Group Algebras ◽  
Skew Group Algebras
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