156 research outputs found
From Quantum Universal Enveloping Algebras to Quantum Algebras
The ``local'' structure of a quantum group G_q is currently considered to be
an infinite-dimensional object: the corresponding quantum universal enveloping
algebra U_q(g), which is a Hopf algebra deformation of the universal enveloping
algebra of a n-dimensional Lie algebra g=Lie(G). However, we show how, by
starting from the generators of the underlying Lie bialgebra (g,\delta), the
analyticity in the deformation parameter(s) allows us to determine in a unique
way a set of n ``almost primitive'' basic objects in U_q(g), that could be
properly called the ``quantum algebra generators''. So, the analytical
prolongation (g_q,\Delta) of the Lie bialgebra (g,\delta) is proposed as the
appropriate local structure of G_q. Besides, as in this way (g,\delta) and
U_q(g) are shown to be in one-to-one correspondence, the classification of
quantum groups is reduced to the classification of Lie bialgebras. The su_q(2)
and su_q(3) cases are explicitly elaborated.Comment: 16 pages, 0 figures, LaTeX fil
Possible contractions of quantum orthogonal groups
Possible contractions of quantum orthogonal groups which correspond to
different choices of primitive elements of Hopf algebra are considered and all
allowed contractions in Cayley--Klein scheme are obtained. Quantum deformations
of kinematical groups have been investigated and have shown that quantum analog
of (complex) Galilei group G(1,3) do not exist in our scheme.Comment: 10 pages, Latex. Report given at XXIII Int. Colloquium on Group
Theoretical Methods in Physics, July 31- August 5, 2000, Dubna (Russia
Coherent and squeezed states of quantum Heisenberg algebras
Starting from deformed quantum Heisenberg Lie algebras some realizations are
given in terms of the usual creation and annihilation operators of the standard
harmonic oscillator. Then the associated algebra eigenstates are computed and
give rise to new classes of deformed coherent and squeezed states. They are
parametrized by deformed algebra parameters and suitable redefinitions of them
as paragrassmann numbers. Some properties of these deformed states also are
analyzed.Comment: 32 pages, 3 figure
Early Death in Two Patients with Acute Promyelocytic Leukemia Presenting the bcr3 Isoform, FLT3-ITD Mutation, and Elevated WT1 Level
Despite major advances in the treatment of acute promyelocytic leukemia (APL), the problem of early death (ED) remains unsolved. Alongside the currently known clinical and hematological risk factors, prognostic significance has been attributed to internal tandem duplication mutations of the fms-like tyrosine kinase-3 (FLT3-ITD), hypogranular variant morphology, and the bcr-3 isoform of PML-RARα. We describe premature death of two patients with the hypogranular variant of APL who presented remarkably high expression levels of Wilms' tumor gene (WT1). Our results point to WT1 as an important prognostic factor of ED that needs to be promptly evaluated in all newly diagnosed cases of APL
Expansions of algebras and superalgebras and some applications
After reviewing the three well-known methods to obtain Lie algebras and
superalgebras from given ones, namely, contractions, deformations and
extensions, we describe a fourth method recently introduced, the expansion of
Lie (super)algebras. Expanded (super)algebras have, in general, larger
dimensions than the original algebra, but also include the Inonu-Wigner and
generalized IW contractions as a particular case. As an example of a physical
application of expansions, we discuss the relation between the possible
underlying gauge symmetry of eleven-dimensional supergravity and the
superalgebra osp(1|32).Comment: Invited lecture delivered at the 'Deformations and Contractions in
Mathematics and Physics Workshop', 15-21 January 2006, Mathematisches
Forschungsinstitut Oberwolfach, German
Deformation of orthosymplectic Lie superalgebra osp(1|2)
Triangular deformation of the orthosymplectic Lie superalgebra osp(1|4) is
defined by chains of twists. Corresponding classical r-matrix is obtained by a
contraction procedure from the trigonometric r-matrix. The carrier space of the
constant r-matrix is the Borel subalgebra.Comment: LaTeX, 8 page
On contractions of classical basic superalgebras
We define a class of orthosymplectic and unitary
superalgebras which may be obtained from and
by contractions and analytic continuations in a similar way as the
special linear, orthogonal and the symplectic Cayley-Klein algebras are
obtained from the corresponding classical ones. Casimir operators of
Cayley-Klein superalgebras are obtained from the corresponding operators of the
basic superalgebras. Contractions of and are regarded as
an examples.Comment: 15 pages, Late
Algebraic structure of the Green's ansatz and its q-deformed analogue
The algebraic structure of the Green's ansatz is analyzed in such a way that
its generalization to the case of q-deformed para-Bose and para-Fermi operators
is becoming evident. To this end the underlying Lie (super)algebraic properties
of the parastatistics are essentially used.Comment: plain TeX, Preprint INRNE-TH-94/4, 13
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