Enveloping algebras by Jacques Dixmier

By Jacques Dixmier

Show description

Read Online or Download Enveloping algebras PDF

Best algebra books

Algebra I Essentials For Dummies

With its use of a number of variables, capabilities, and formulation algebra may be complicated and overwhelming to benefit and straightforward to overlook. ideal for college students who have to assessment or reference severe innovations, Algebra I necessities For Dummies presents content material concerned about key themes simply, with discrete causes of severe recommendations taught in a standard Algebra I path, from capabilities and FOILs to quadratic and linear equations.

CK-12 Basic Algebra, Volume 2

CK-12 Foundation's easy Algebra, quantity 2 of two FlexBook covers the subsequent six chapters:Systems of Equations and Inequalities; Counting tools - introduces scholars to linear structures of equations and inequalities in addition to chance and mixtures. Operations on linear structures are lined, together with addition, subtraction, multiplication, and department.

Extra resources for Enveloping algebras

Sample text

2 Property (T) and Fell’s topology 35 and a + b = 1. We then have ϕ = aψ + bψ . We claim that either b = 0 or ψ = 0. Indeed, assume by contradiction that b = 0 and ψ (e) = 0. Then ψ (e) = 1, since ϕ(e) = 1 and ψ(e) ≤ 1, ψ (e) ≤ 1. 6 that limi ψi = ψ uniformly on compact subsets of G. 8 shows that ψ is a sum of functions of positive type associated to π0 . 1) and this is a contradiction. Therefore, we have limi ai ψi = ϕ and limi ai = 1. Thus, limi ψi = ϕ in the weak* topology; by Raikov’s Theorem, this holds also uniformly on compact subsets of G.

12). 12 again. Since π0 ⊗ π 0 = π1 ⊕ · · · ⊕ πn , it follows that σi is unitarily equivalent to one of the πk ’s. This is a contradiction to the choice of (σi )i∈I . P. 1]. 3 Compact generation and other consequences The first spectacular application of Property (T) is the following result, due to Kazhdan. 1 Let G be a locally compact group with Property (T). Then G is compactly generated. In particular, a discrete group with Property (T) is finitely generated. 3 Compact generation and other consequences 37 Proof Let C be the set of all open and compactly generated subgroups of G.

Indeed, SLn (Q) is not finitely generated, since every finite subset {x1 , . . , xm } of SLn (Q) is contained in SLn (Z[1/N ]), where N is a common multiple of the denominators of the matrix coefficients of x1 , . . , xm . 1. 4 Property (T) for SLn (K), n ≥ 3 Let K be a local field . 4, for more details). 6). 4. Some general facts We collect the common ingredients used in the proofs of Property (T) for SLn (K) and Sp2n (K). 1 Let G be a topological group, and let (π , H) be a unitary representation of G with 1G ≺ π.

Download PDF sample

Rated 4.88 of 5 – based on 42 votes