241 research outputs found

### Quantization of Holomorphic Poisson structure --related to Generalized K\"{a}hler structure--

It is known that holomorphic Poisson structures are closely related to
theories of generalized K\"{a}hler geometry and bi-Hermitian structures. In
this article, we introduce quantization of holomorphic Poisson structures which
are closely related to generalized K\"{a}hler structures /bi-Hermitian
structures. By resulting noncommutative product $\star$ obtained via
quantization, we also demonstrate computations with respect to concrete
examples.Comment: arXiv admin note: text overlap with arXiv:1304.018

### Automorphisms of the Weyl manifold

Assume that $M$ is a smooth manifold with a symplectic structure $\omega$.
Then Weyl manifolds on the symplectic manifold $M$ are Weyl algebra bundles
endowed with suitable transition functions. From the geometrical point of view,
Weyl manifolds can be regarded as geometrizations of star products attached to
$(M,\omega)$. In the present paper, we are concerned with the automorphisms of
the Weyl manifold corresponding to Poincar\'e-Cartan class ($c_0$ is a
$\check{\rm C}$ech cocycle corresponding to the symplectic structure $\omega$.)
$[c_0+\sum_{\ell=1}^\infty c_{\ell} \nu^{2\ell}]\in \check{H}^2 (M)[[\nu^2]]$.
We also construct modified contact Weyl diffeomorphisms

### Symbol calculus on a projective space

In this article, we introduce symbol calculus on a projective scheme. Using
holomorphic Poisson structures, we construct deformations of ring structures
for structure sheaves on projective spaces

### Formal Deformation Quantization for Super Poisson Structures on Super Calabi-Yau Twistor Spaces

It is known that Wolf constructed a lot of examples of Super Calabi-Yau
twistor spaces. We would like to introduce super Poisson structures on them via
super twistor double fibrations. Moreover we define the structure of
deformation quantization for such super Poisson manifolds

### Deformation Expression for Elements of Algebras (VIII) --SU(2)-vacuum and the regular representation space--

Consider the problem "Give the equation of the conceptional rotations in
${\mathbb R}^3$ without using the parameter expressing individual rotations",
just as the conceptional motion of constant velocity along straight lines
(Galiley motions) is expressed by an elementary differential equation. In this
we try to give an answer to the topic related with the above issue

### Deformation Expression for Elements of Algebras (VI) --Vacuum representation of Heisenberg algebra--

The Weyl algebra (W_{2m}[h]; *) is the algebra generated by
u=(u_1,...,u_m,v_1,.....,v_m) over C with the fundamental commutation relation
[u_i,v_j]=-ih\delta_{ij}, where h is a positive constant. The Heisenberg
algebra (\Cal H_{2m}[nu];*) is the algebra given by regarding the scalar
parameter h in the Weyl algebra W_{2m}[h] to be a generator nu which commutes
with all others

### Deformation Expression for Elements of Algebras (II) --(Weyl algebra of 2m-generators)--

This is a noncommutative version of the previous work entitled "Deformation
Expression for Elements of Algebras (I)." In general in a noncommutative
algebra, there is no canonical way to express elements in univalent way, which
is often called "ordering problem". In this note we discuss this problem in the
case of the Weyl algebra of 2m-generators. By fixing an expression, we extends
Weyl algebra transcendentally. We treat *-exponential functions of linear
forms, and quadratic forms of crossed symbol under generic expression
parameters

### Deformation Expression for Elements of Algebras (I) --(Jacobi's theta functions and *-exponential functions)--

This paper presents a preliminary version of the deformation theory of
expressions of elements of algebras. The notion of *-functions is given.
Several important problems appear in simplified forms, and these give an
intuitive bird's-eye of the whole theory

### Deformation Expression for Elements of Algebras (V) - Diagonal matrix calculus and $*$-special functions -

In this note, we are interested in the *-version of various special
functions. Noting that many special functions are defined by integrals
involving the exponential functions, we define *-special functions by similar
integral formula replacing exponential functions by *-exponential functions

### Geometric objects in an approach to quantum geometry

Ideas from deformation quantization applied to algebras with one generator
lead to methods to treat a nonlinear flat connection. It provides us elements
of algebras to be parallel sections. The moduli space of the parallel sections
is studied as an example of bundle-like objects with discordant (sogo)
transition functions, which suggests us to treat movable branching
singularities

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