SQUARES OF WHITE NOISE, SL(2, ℂ) AND KUBO–MARTIN–SCHWINGER STATES

2006 ◽  
Vol 09 (04) ◽  
pp. 491-511 ◽  
Author(s):  
DMITRY V. PROKHORENKO
Keyword(s):  
White Noise ◽  
Universal Enveloping Algebra ◽  
Half Line ◽  
Probability Measures ◽  
Kms States ◽  
The Real ◽  
Enveloping Algebra ◽  
One To One

We investigate the structure of Kubo–Martin–Schwinger (KMS) states on some extension of the universal enveloping algebra of SL (2, ℂ). We find that there exists a one-to-one correspondence between the set of all covariant KMS states on this algebra and the set of all probability measures dμ on the real half-line [0, +∞), which decrease faster than any inverse polynomial. This problem is connected to the problem of KMS states on square of white noise algebra.

scholarly journals Irreducible Representations of Algebras

1974 ◽  
Vol 26 (5) ◽  
pp. 1118-1129 ◽  
Author(s):  
Edgar G. Goodaire
Keyword(s):  
Associative Algebra ◽  
Universal Enveloping Algebra ◽  
Irreducible Representations ◽  
Enveloping Algebra ◽  
Representations Of Algebras ◽  
One To One

The concept of the universal enveloping algebra of a (not necessarily associative) algebra X is basic to the study of the representations of X, because there is a one-to-one correspondence between the representations of X and . If one is only interested in studying a certain class of the representations of X, the thought occurs that there may exist a more suitable universal object.

scholarly journals DG Poisson algebra and its universal enveloping algebra

2016 ◽  
Vol 59 (5) ◽  
pp. 849-860 ◽  
Author(s):  
JiaFeng Lü ◽  
XingTing Wang ◽  
GuangBin Zhuang
Keyword(s):  
Poisson Algebra ◽  
Universal Enveloping Algebra ◽  
Enveloping Algebra

scholarly journals The Wiener-Pitt Phenomenon on the Half-Line

1962 ◽  
Vol 13 (1) ◽  
pp. 37-38 ◽  
Author(s):  
J. H. Williamson
Keyword(s):  
Real Line ◽  
Half Line ◽  
Stieltjes Transform ◽  
The Real

It has been well known for many years (2) that if Fμ(t) is the Fourier-Stieltjes transform of a bounded measure μ on the real line R, which is bounded away from zero, it does not follow that [Fμ(t)]−1 is also the Fourier-Stieltjes transform of a measure. It seems of interest (as was remarked, in conversation, by J. D. Weston) to consider measures on the half-line R+ = [0, ∞[, instead of on R.

scholarly journals ELEMENTARY INVARIANTS FOR CENTRALIZERS OF NILPOTENT MATRICES

2009 ◽  
Vol 86 (1) ◽  
pp. 1-15 ◽  
Author(s):  
JONATHAN BROWN ◽  
JONATHAN BRUNDAN
Keyword(s):  
Lie Algebra ◽  
Characteristic Zero ◽  
Universal Enveloping Algebra ◽  
General Linear ◽  
Enveloping Algebra ◽  
Nilpotent Matrix ◽  
Nilpotent Matrices ◽  
Algebra Over A Field

AbstractWe construct an explicit set of algebraically independent generators for the center of the universal enveloping algebra of the centralizer of a nilpotent matrix in the general linear Lie algebra over a field of characteristic zero. In particular, this gives a new proof of the freeness of the center, a result first proved by Panyushev, Premet and Yakimova.

Sign in / Sign up

Export Citation Format

Share Document