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Paper's Title:
Bartle Integration in Lie Algebras
Author(s):
Andreas Boukas and Philip Feinsilver
Centro Vito Volterra,
Universita di Roma Tor Vergata,
via Columbia 2, 00133 Roma,
Italy.
Department of Mathematics,
Southern Illinois University,
Carbondale, Illinois 62901,
USA.
E-mail:
andreasboukas@yahoo.com
E-mail: pfeinsil@math.siu.edu
Abstract:
Using Bartle's bilinear vector integral we define stochastic integrals of bounded operator valued functions with respect to Stieltjes measures associated with the generators of the Heisenberg and Finite Difference Lie algebras. Our definition also covers the Square of White Noise and sl/2 Lie algebras.
Paper's Title:
On the Fock Representation of the Central Extensions of the Heisenberg Algebra
Author(s):
L. Accardi and A. Boukas
Centro Vito Volterra, Universitą di Roma
Tor Vergata,
via Columbia 2, 00133 Roma,
Italy
accardi@volterra.mat.uniroma2.it
URL: http://volterra.mat.uniroma2.it
Department of Mathematics,
American College of Greece,
Aghia Paraskevi, Athens 15342,
Greece
andreasboukas@acg.edu
Abstract:
We examine the possibility of a direct Fock representation of
the recently obtained non-trivial central extensions
of the Heisenberg algebra, generated by elements
and
E satisfying the commutation relations
,
and
,
where a and
are dual, h is self-adjoint, E is the non-zero self-adjoint
central element and
We define the exponential vectors associated with the
Fock space, we compute their Leibniz function (inner product), we describe the
action of a,
and h on the exponential vectors and we compute the moment generating and
characteristic functions of the classical random variable corresponding to the
self-adjoint operator
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