scholarly journals On the BV structure of the Hochschild cohomology of finite group algebras

2021 ◽  
Vol 313 (1) ◽  
pp. 1-44
Author(s):  
Dave Benson ◽  
Radha Kessar ◽  
Markus Linckelmann
Keyword(s):  
Finite Group ◽  
Hochschild Cohomology ◽  
Group Algebras

scholarly journals Bockstein homomorphisms for Hochschild cohomology of group algebras and of block algebras of finite groups

2017 ◽  
Vol 29 (3) ◽  
Author(s):  
Constantin-Cosmin Todea
Keyword(s):  
Finite Group ◽  
Group Algebra ◽  
Finite Groups ◽  
Hochschild Cohomology ◽  
Product Formula ◽  
Group Algebras ◽  
Closed Field ◽  
Additive Decomposition ◽  
A Finite Group ◽  
Block Algebra

AbstractWe give an explicit approach for Bockstein homomorphisms of the Hochschild cohomology of a group algebra and of a block algebra of a finite group and we show some properties. To give explicit definitions for these maps we use an additive decomposition and a product formula for the Hochschild cohomology of group algebras given by Siegel and Witherspoon in 1999. For an algebraically closed field

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.

scholarly journals Universal fields of fractions for polycyclic group algebras

1982 ◽  
Vol 23 (2) ◽  
pp. 103-113 ◽  
Author(s):  
D. S. Passman
Keyword(s):  
Finite Group ◽  
Prime Ideal ◽  
Group Algebra ◽  
Quotient Ring ◽  
Polycyclic Group ◽  
Group Algebras ◽  
Completely Prime Ideal

Let G be a polycyclic-by-finite group and let K[G] denote its group algebra over the field K. In this paper we discuss localization in K[G] and in particular we prove that every faithful completely prime ideal is localizable. Furthermore, using a sequence of localizations, we show that, for G polyinfinite cyclic, the classical right quotient ring (K[G]) is in fact a universal field of fractions for K[G]. Finally we offer an example of a domain K[G] which does not have a universal field of fractions.

scholarly journals Polycyclic-by-finite group algebras are catenary

1999 ◽  
Vol 6 (2) ◽  
pp. 183-194 ◽  
Author(s):  
Edward S. Letzter ◽  
Martin Lorenz
Keyword(s):  
Finite Group ◽  
Group Algebras

scholarly journals Group algebras whose p-elements form a subgroup

2016 ◽  
Vol 16 (09) ◽  
pp. 1750170
Author(s):  
M. Ramezan-Nassab
Keyword(s):  
Finite Group ◽  
Normal Subgroup ◽  
Group Algebra ◽  
Polynomial Identity ◽  
Matrix Polynomial ◽  
Unit Group ◽  
Group Algebras ◽  
Locally Finite ◽  
P Elements

Let [Formula: see text] be a group, [Formula: see text] a field of characteristic [Formula: see text], and [Formula: see text] the unit group of the group algebra [Formula: see text]. In this paper, among other results, we show that if either (1) [Formula: see text] satisfies a non-matrix polynomial identity, or (2) [Formula: see text] is locally finite, [Formula: see text] is infinite and [Formula: see text] is an Engel-by-finite group, then the [Formula: see text]-elements of [Formula: see text] form a (normal) subgroup [Formula: see text] and [Formula: see text] is abelian (here, of course, [Formula: see text] if [Formula: see text]).

The nilpotency index of the radicals of group algebras of finite groups whose Sylow 3-subgroups are extra-special of order 27 of exponent 3

1988 ◽  
Vol 108 (1-2) ◽  
pp. 117-132
Author(s):  
Shigeo Koshitani
Keyword(s):  
Finite Group ◽  
Normal Subgroup ◽  
Positive Integer ◽  
Simple Group ◽  
Finite Groups ◽  
Jacobson Radical ◽  
Group Algebras ◽  
Nilpotency Index ◽  
Characteristic 3 ◽  
A Finite Group

SynopsisLet J(FG) be the Jacobson radical of the group algebra FG of a finite groupG with a Sylow 3-subgroup which is extra-special of order 27 of exponent 3 over a field F of characteristic 3, and let t(G) be the least positive integer t with J(FG)t = 0. In this paper, we prove that t(G) = 9 if G has a normal subgroup H such that (|G:H|, 3) = 1 and if H is either 3-solvable, SL(3,3) or the Tits simple group 2F4(2)'.

scholarly journals A classification of exceptional components in group algebras over abelian number fields

2016 ◽  
Vol 15 (05) ◽  
pp. 1650092
Author(s):  
Andreas Bächle ◽  
Mauricio Caicedo ◽  
Inneke Van Gelder
Keyword(s):  
Finite Group ◽  
Unit Group ◽  
Number Fields ◽  
Group Algebras ◽  
Matrix Rings ◽  
Division Rings ◽  
Wedderburn Decomposition ◽  
A Finite Group

When considering the unit group of [Formula: see text] ([Formula: see text] the ring of integers of an abelian number field [Formula: see text] and a finite group [Formula: see text]) certain components in the Wedderburn decomposition of [Formula: see text] cause problems for known generic constructions of units; these components are called exceptional. Exceptional components are divided into two types: type 1 is division rings, type 2 is [Formula: see text]-matrix rings. For exceptional components of type 1 we provide infinite classes of division rings by describing the seven cases of minimal groups (with respect to quotients) having those division rings in their Wedderburn decomposition over [Formula: see text]. We also classify the exceptional components of type 2 appearing in group algebras of a finite group over number fields [Formula: see text] by describing all 58 finite groups [Formula: see text] having a faithful exceptional Wedderburn component of this type in [Formula: see text].

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