226 research outputs found
Non-rationality of some fibrations associated to Klein surfaces
We study the polynomial fibration induced by the equation of the Klein
surfaces obtained as quotient of finite linear groups of automorphisms of the
plane; this surfaces are of type A, D, E, corresponding to their singularities.
The generic fibre of the polynomial fibration is a surface defined over the
function field of the line. We proved that it is not rational in cases D, E,
although it is obviously rational in the case A.
The group of automorphisms of the Klein surfaces is also described, and is
linear and of finite dimension in cases D, E; this result being obviously false
in case A.Comment: 18 page
The anticommutator spin algebra, its representations and quantum group invariance
We define a 3-generator algebra obtained by replacing the commutators by
anticommutators in the defining relations of the angular momentum algebra. We
show that integer spin representations are in one to one correspondence with
those of the angular momentum algebra. The half-integer spin representations,
on the other hand, split into two representations of dimension j + 1/2. The
anticommutator spin algebra is invariant under the action of the quantum group
SO_q(3) with q=-1.Comment: 7 A4 page
Mirror symmetry and quantization of abelian varieties
The paper consists of two sections. The first section provides a new
definition of mirror symmetry of abelian varieties making sense also over
-adic fields. The second section introduces and studies quantized
theta-functions with two-sided multipliers, which are functions on
non-commutative tori. This is an extension of an earlier work by the author. In
the Introduction and in the Appendix the constructions of this paper are put
into a wider context.Comment: 24 pp., amstex file, no figure
Quantum Mechanics on the h-deformed Quantum Plane
We find the covariant deformed Heisenberg algebra and the Laplace-Beltrami
operator on the extended -deformed quantum plane and solve the Schr\"odinger
equations explicitly for some physical systems on the quantum plane. In the
commutative limit the behaviour of a quantum particle on the quantum plane
becomes that of the quantum particle on the Poincar\'e half-plane, a surface of
constant negative Gaussian curvature. We show the bound state energy spectra
for particles under specific potentials depend explicitly on the deformation
parameter . Moreover, it is shown that bound states can survive on the
quantum plane in a limiting case where bound states on the Poincar\'e
half-plane disappear.Comment: 16pages, Latex2e, Abstract and section 4 have been revise
Research potential as a basis for innovative development of the region
Purpose of work is to determine an amount of influence from region’s innovative activity on effective usage of current scientific-research potential. Innovative activity of regions in many respects depends on the availability and efficient use of the existing research capacity. The main components of the research capacities in the region are: interest of universities, employers and society in research and development and their implementation in practice; development of research infrastructure; and a focus of higher education on the innovative activity of students; financial and tax support of enterprises engaged in innovative activities, from the stat
Aspects of a new class of braid matrices: roots of unity and hyperelliptic for triangularity, L-algebra,link-invariants, noncommutative spaces
Various properties of a class of braid matrices, presented before, are
studied considering vector representations for two
subclasses. For the matrices are nontrivial. Triangularity corresponds to polynomial equations for , the solutions ranging from
roots of unity to hyperelliptic functions. The algebras of operators are
studied. As a crucial feature one obtains central, group-like, homogenous
quadratic functions of constrained to equality among themselves by the
equations. They are studied in detail for and are proportional to
for the fundamental representation and hence for all iterated
coproducts. The implications are analysed through a detailed study of the
representation for N=3. The Turaev construction for link invariants
is adapted to our class. A skein relation is obtained. Noncommutative spaces
associated to our class of are constructed. The transfer matrix map is
implemented, with the N=3 case as example, for an iterated construction of
noncommutative coordinates starting from an dimensional commutative
base space. Further possibilities, such as multistate statistical models, are
indicated.Comment: 34 pages, pape
Duality for the Jordanian Matrix Quantum Group
We find the Hopf algebra dual to the Jordanian matrix quantum group
. As an algebra it depends only on the sum of the two parameters
and is split in two subalgebras: (with three generators) and
(with one generator). The subalgebra is a central Hopf subalgebra of
. The subalgebra is not a Hopf subalgebra and its coalgebra
structure depends on both parameters. We discuss also two one-parameter special
cases: and . The subalgebra is a Hopf algebra and
coincides with the algebra introduced by Ohn as the dual of . The
subalgebra is isomorphic to as an algebra but has a
nontrivial coalgebra structure and again is not a Hopf subalgebra of
.Comment: plain TeX with harvmac, 16 pages, added Appendix implementing the ACC
nonlinear ma
Q-Boson Representation of the Quantum Matrix Algebra
{Although q-oscillators have been used extensively for realization of quantum
universal enveloping algebras,such realization do not exist for quantum matrix
algebras ( deformation of the algebra of functions on the group ). In this
paper we first construct an infinite dimensional representation of the quantum
matrix algebra (the coordinate ring of and then use
this representation to realize by q-bosons.}Comment: pages 18 ,report # 93-00
Representations of the quantum matrix algebra
It is shown that the finite dimensional irreducible representaions of the
quantum matrix algebra ( the coordinate ring of ) exist only when both q and p are roots of unity. In this case th e space of
states has either the topology of a torus or a cylinder which may be thought of
as generalizations of cyclic representations.Comment: 20 page
Graded q-pseudo-differential Operators and Supersymmetric Algebras
We give a supersymmetric generalization of the sine algebra and the quantum
algebra . Making use of the -pseudo-differential operators
graded with a fermionic algebra, we obtain a supersymmetric extension of sine
algebra. With this scheme we also get a quantum superalgebra .Comment: 10 pages, Late
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