Hochschild cohomology of the integral group ring of a cyclic group and related algebras

1996 ◽  
Vol 67 (5) ◽  
pp. 360-366 ◽  
Author(s):  
Thorsten Holm
Keyword(s):  
Cyclic Group ◽  
Group Ring ◽  
Hochschild Cohomology ◽  
Integral Group Ring ◽  
Integral Group

Lehmer’s problem for arbitrary groups

2020 ◽  
pp. 1-32
Author(s):  
W. Lück
Keyword(s):  
Cyclic Group ◽  
Group Ring ◽  
Bounded Operator ◽  
Integral Group Ring ◽  
Integral Group ◽  
Infinite Cyclic Group ◽  
Matrix Formula ◽  
Lehmer’S Problem

We consider the problem whether for a group [Formula: see text] there exists a constant [Formula: see text] such that for any [Formula: see text]-matrix [Formula: see text] over the integral group ring [Formula: see text] the Fuglede–Kadison determinant of the [Formula: see text]-equivariant bounded operator [Formula: see text] given by right multiplication with [Formula: see text] is either one or greater or equal to [Formula: see text]. If [Formula: see text] is the infinite cyclic group and we consider only [Formula: see text], this is precisely Lehmer’s problem.

Hochschild Cohomology Ring of the Integral Group Ring of the Semidihedral 2-Group

2011 ◽  
Vol 18 (02) ◽  
pp. 241-258 ◽  
Author(s):  
Takao Hayami
Keyword(s):  
Group Ring ◽  
Hochschild Cohomology ◽  
Cohomology Ring ◽  
Ring Structure ◽  
Integral Group Ring ◽  
Integral Group ◽  
Hochschild Cohomology Ring

We determine the ring structure of the Hochschild cohomology HH*(ℤ G) of the integral group ring of the semidihedral 2-group G = SD2r of order 2r.

scholarly journals Whitehead groups of semidirect products of free groups

1978 ◽  
Vol 19 (2) ◽  
pp. 155-158 ◽  
Author(s):  
Koo-Guan Choo
Keyword(s):  
Cyclic Group ◽  
Group Ring ◽  
Semidirect Product ◽  
Class Group ◽  
Integral Group Ring ◽  
Integral Group ◽  
Whitehead Group ◽  
Infinite Cyclic Group ◽  
Semidirect Products ◽  
Projective Class

Let G be a group. We denote the Whitehead group of G by Wh G and the projective class group of the integral group ring ℤ(G) of G by . Let α be an automorphism of G and T an infinite cyclic group. Then we denote by G ×αT the semidirect product of G and T with respect to α. For undefined terminologies used in the paper, we refer to [3] and [7].

On Hochschild cohomology ring and integral cohomology ring for the semidihedral group

2018 ◽  
Vol 28 (02) ◽  
pp. 257-290
Author(s):  
Takao Hayami
Keyword(s):  
Group Ring ◽  
Hochschild Cohomology ◽  
Cohomology Ring ◽  
Ring Structure ◽  
Integral Group Ring ◽  
Integral Group ◽  
Precise Description ◽  
Arbitrary Integer ◽  
Integral Cohomology ◽  
Hochschild Cohomology Ring

We will determine the ring structure of the Hochschild cohomology [Formula: see text] of the integral group ring of the semidihedral group [Formula: see text] of order [Formula: see text] for arbitrary integer [Formula: see text] by giving the precise description of the integral cohomology ring [Formula: see text] and by using a method similar to [T. Hayami, Hochschild cohomology ring of the integral group ring of the semidihedral [Formula: see text]-group, Algebra Colloq. 18 (2011) 241–258].

Sign in / Sign up

Export Citation Format

Share Document