scholarly journals Free group algebras in Malcev–Neumann skew fields of fractions

2014 ◽  
Vol 26 (2) ◽  
Author(s):  
Javier Sánchez
Keyword(s):  
Free Group ◽  
Group Algebras ◽  
Skew Fields

AbstractLet

FREE GROUP ALGEBRAS IN DIVISION RINGS

2012 ◽  
Vol 22 (05) ◽  
pp. 1250044 ◽  
Author(s):  
J. Z. GONÇALVES ◽  
E. TENGAN
Keyword(s):  
Free Group ◽  
Infinite Order ◽  
Algebraic Function ◽  
Group Algebras ◽  
Closed Field ◽  
Skew Polynomial Ring ◽  
Algebraic Function Field ◽  
Skew Field ◽  
Rank 2 ◽  
Skew Polynomial

Let k be an algebraically closed field of characteristic zero and let L be an algebraic function field over k. Let σ : L → L be a k-automorphism of infinite order, and let D be the skew field of fractions of the skew polynomial ring L[t; σ]. We show that D contains the group algebra kF of the free group F of rank 2.

Relative amenability and the non-amenability of B(l1)

2006 ◽  
Vol 80 (3) ◽  
pp. 317-333
Author(s):  
C. J. Read
Keyword(s):  
Banach Algebra ◽  
Free Group ◽  
Direct Proof ◽  
Group Algebras ◽  
Direct Sums ◽  
Matrix Algebras ◽  
Direct Sum ◽  
Symmetric Basis ◽  
Finite Dimensional ◽  
Finite Dimensional Algebras

AbstractIn this paper we begin with a short, direct proof that the Banach algebra B(l1) is not amenable. We continue by showing that various direct sums of matrix algebras are not amenable either, for example the direct sum of the finite dimensional algebras is no amenable for 1 ≤ p ≤ ∞, p ≠ 2. Our method of proof naturally involves free group algebras, (by which we mean certain subalgebras of B(X) for some space X with symmetric basis—not necessarily X = l2) and we introduce the notion of ‘relative amenability’ of these algebras.

scholarly journals Group algebras of some generalised soluble groups

1972 ◽  
Vol 18 (1) ◽  
pp. 1-5 ◽  
Author(s):  
R. P. Knott
Keyword(s):  
Free Group ◽  
Group Algebra ◽  
Soluble Group ◽  
Group Algebras ◽  
Soluble Groups ◽  
Torsion Free Group ◽  
Open Question ◽  
Torsion Free

In (8) Stonehewer referred to the following open question due to Amitsur: If G is a torsion-free group and F any field, is the group algebra, FG, of G over F semi-simple? Stonehewer showed the answer was in the affirmative if G is a soluble group. In this paper we show the answer is again in the affirmative if G belongs to a class of generalised soluble groups

Sign in / Sign up

Export Citation Format

Share Document