37 research outputs found
Second N=1 Superanalog of Complex Structure
We found another N=1 odd superanalog of complex structure (the even one is
widely used in the theory of super Riemann surfaces). New N=1
superconformal-like transformations are similar to anti-holomorphic ones of
nonsupersymmetric complex function theory. They are dual to the ordinary
superconformal transformations subject to the Berezinian addition formula
presented, noninvertible, highly degenerated and twist parity of the tangent
space in the standard basis. They also lead to the ''mixed cocycle condition''
which can be used in building noninvertible objects analogous to super Riemann
surfaces. A new parametrization for the superconformal group is presented which
allows us to extend it to a semigroup and to unify the description of old and
new transformations.Comment: 9 pages, Standard LaTe
On Uq (sl2)-actions on the Quantum Plane
To give the complete list of Uq (sl2)-actions of the quantum plane, we first obtain the structure of quantum plane automorphisms. Then we introduce some special symbolic matrices to classify the series of actions using the weights. There are uncountably many isomorphism classes of the symmetries. We give the classical limit of the above actions
Regular obstructed categories and TQFT
A proposal of the concept of -regular obstructed categories is given. The
corresponding regularity conditions for mappings, morphisms and related
structures in categories are considered. An n-regular TQFT is introduced. It is
shown the connection of time reversibility with the regularity.Comment: 22 pages in Latex. To be published in J. Math. Phy
Differential Calculus on -Deformed Light-Cone
We propose the ``short'' version of q-deformed differential calculus on the
light-cone using twistor representation. The commutation relations between
coordinates and momenta are obtained. The quasi-classical limit introduced
gives an exact shape of the off-shell shifting.Comment: 11 pages, Standard LaTeX 2.0
On Alternative Supermatrix Reduction
We consider a nonstandard odd reduction of supermatrices (as compared with
the standard even one) which arises in connection with possible extension of
manifold structure group reductions. The study was initiated by consideration
of the generalized noninvertible superconformal-like transformations. The
features of even- and odd-reduced supermatrices are investigated on a par. They
can be unified into some kind of "sandwich" semigroups. Also we define a
special module over even- and odd-reduced supermatrix sets, and the generalized
Cayley-Hamilton theorem is proved for them. It is shown that the odd-reduced
supermatrices represent semigroup bands and Rees matrix semigroups over a unit
group.Comment: 22 pages, Standard LaTeX with AmS font
Generalized Duality, Hamiltonian Formalism and New Brackets
It is shown that any singular Lagrangian theory: 1) can be formulated without the use of constraints by introducing a Clairaut-type version of the Hamiltonian formalism; 2) leads to a special kind of nonabelian gauge theory which is similar to the Poisson gauge theory; 3) can be treated as the many-time classical dynamics. A generalization of the Legendre transform to the zero Hessian case is done by using the mixed(envelope/general) solution of the multidimensional Clairaut equation. The equations of motion are written in the Hamilton-like form by introducing new antisymmetric brackets. It is shown that any classical degenerate Lagrangian theory is equivalent to the many-time classical dynamics. Finally, the relation between the presented formalism and the Dirac approach to constrained systems is given.Показано, что любая сингулярная лагранжева теория: 1) может быть сформулирована без привлечения связей с помощью Клеро-версии гамильтонового формализма; 2) приводит к специальному виду неабелевой калибровочной теории, которая подобна пуассоновой калибровочной теории; 3) может быть сформулирована как многовременная классическая динамика. Обобщение преобразования Лежандра на случай нулевого гессиана проведено с использованием смешанного (обертывающего/общего) решения многомерного уравнения Клеро. Уравнения движения записываются в гамильтоновой форме с помощью введения новых антисимметричных скобок. Отмечено, что любая классическая система с вырожденным лагранжианом эквивалентна многовременной классической динамике. В заключение приведено взаимоотношение представленного формализма и теории связей Дирака
Classification of Uq(sl₂)-Module Algebra Structures on the Quantum Plane
A complete list of Uq(sl₂)-module algebra structures on the quantum plane is produced and the (uncountable family of) isomorphism classes of these structures are described. The composition series of representations in question are computed. The classical limits of the Uq(sl₂)-module algebra structures are discussed
Conformal symmetry transformations and nonlinear Maxwell equations
We make use of the conformal compactification of Minkowski spacetime
to explore a way of describing general, nonlinear Maxwell fields with conformal
symmetry. We distinguish the inverse Minkowski spacetime
obtained via conformal inversion, so as to discuss a doubled compactified
spacetime on which Maxwell fields may be defined. Identifying with the
projective light cone in -dimensional spacetime, we write two
independent conformal-invariant functionals of the -dimensional Maxwellian
field strength tensors -- one bilinear, the other trilinear in the field
strengths -- which are to enter general nonlinear constitutive equations. We
also make some remarks regarding the dimensional reduction procedure as we
consider its generalization from linear to general nonlinear theories.Comment: 12 pages, Based on a talk by the first author at the International
Conference in Mathematics in honor of Prof. M. Norbert Hounkonnou (October
29-30, 2016, Cotonou, Benin). To be published in the Proceedings, Springer
201
SOME ABSTRACT PROPERTIES OF SEMIGROUPS APPEARING IN SUPERCONFORMAL THEORIES
A new type of semigroups which appears while dealing with
superconformal symmetry in superstring theories is considered. The ideal series
having unusual abstract properties is constructed. Various idealisers are
introduced and studied. The ideal quasicharacter is defined. Green's relations
are found and their connection with the ideal quasicharacter is established.Comment: 11 page