Quantizations of Flag Manifolds and Conformal Space Time

1997 ◽  
Vol 09 (04) ◽  
pp. 453-465 ◽  
Author(s):  
R. Fioresi
Keyword(s):  
Euclidean Space ◽  
Minkowski Space ◽  
Conformal Group ◽  
Flag Manifolds ◽  
The Real ◽  
Rham Complex ◽  
De Rham ◽  
Big Cell ◽  
Real Complex ◽  
Real Euclidean Space

In this paper we work out the deformations of some flag manifolds and of complex Minkowski space viewed as an affine big cell inside G(2,4). All the deformations come in tandem with a coaction of the appropriate quantum group. In the case of the Minkowski space this allows us to define the quantum conformal group. We also give two involutions on the quantum complex Minkowski space, that respectively define the real Minkowski space and the real euclidean space. We also compute the quantum De Rham complex for both real (complex) Minkowski and euclidean space.

On Certain Functional Identities in EN

1971 ◽  
Vol 23 (2) ◽  
pp. 315-324 ◽  
Author(s):  
A. McD. Mercer
Keyword(s):  
Euclidean Space ◽  
Taylor Series ◽  
Dimensional Space ◽  
The Real ◽  
Higher Dimensional ◽  
Isolated Points ◽  
Functional Identities ◽  
Image Position ◽  
Special Case ◽  
Real Euclidean Space

1. If f is a real-valued function possessing a Taylor series convergent in (a — R, a + R), then it satisfies the following operational identity1.1in which D2 = d2/du2. Furthermore, when g is a solution of y″ + λ2y = 0 in (a – R, a + R), then g is such a function and (1.1) specializes to1.2In this note we generalize these results to the real Euclidean space EN, our conclusions being Theorems 1 and 2 below. Clearly, (1.2) is a special case of (1.1) but in higher-dimensional space it is of interest to allow g, now a solution of1.3to possess singularities at isolated points away from the origin. It is then necessary to consider not only a neighbourhood of the origin but annular regions also.

scholarly journals De Rham complex for quantized irreducible flag manifolds

2006 ◽  
Vol 305 (2) ◽  
pp. 704-741 ◽  
Author(s):  
István Heckenberger ◽  
Stefan Kolb
Keyword(s):  
Flag Manifolds ◽  
De Rham Complex ◽  
Rham Complex ◽  
De Rham

scholarly journals MULTIDIMENSIONAL HYBRID BOUNDARY VALUE PROBLEM

2018 ◽  
Vol 58 (6) ◽  
pp. 402-413
Author(s):  
Marzena Szajewska ◽  
Agnieszka Maria Tereszkiewicz
Keyword(s):  
Euclidean Space ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Special Functions ◽  
Boundary Value ◽  
Fundamental Region ◽  
The Real ◽  
Real Euclidean Space

The purpose of this paper is to discuss three types of boundary conditions for few families of special functions orthogonal on the fundamental region. Boundary value problems are considered on a simplex F in the real Euclidean space Rn of dimension n > 2.

A Banach Space Whose Elements are Classes of Sets of Constant Width

1975 ◽  
Vol 18 (5) ◽  
pp. 679-689 ◽  
Author(s):  
J. E. Lewis
Keyword(s):  
Banach Space ◽  
Euclidean Space ◽  
Compact Subset ◽  
Compact Convex ◽  
Constant Width ◽  
The Real ◽  
Real Euclidean Space ◽  
Convex Subsets

Let K be a compact subset of the real Euclidean space En. We say that K has constant width if the distance between each pair of distinct parallel hyperplanes which support K is constant. The collection of all compact convex subsets of En which have constant width is denoted .

A DEFORMATION OF THE BIG CELL INSIDE THE GRASSMANNIAN MANIFOLD G(r,n)

1999 ◽  
Vol 11 (01) ◽  
pp. 25-40 ◽  
Author(s):  
R. FIORESI
Keyword(s):  
Homogeneous Space ◽  
Parabolic Subgroup ◽  
Differential Operators ◽  
De Rham Complex ◽  
Grassmannian Manifold ◽  
Quantum Analogue ◽  
Rham Complex ◽  
Quantum Homogeneous Space ◽  
De Rham ◽  
Big Cell

In this paper we construct a quantum analogue of the big cell inside the grassmannian manifold. Our deformation comes in tandem with a coaction of the upper parabolic subgroup in SLn(k), giving to the big cell the structure of quantum homogeneous space. At the end we give the De Rham complex of the quantum big cell and we define a ring of differential operators acting on the quantum big cell.

scholarly journals Integral calculus on quantum exterior algebras

2014 ◽  
Vol 11 (04) ◽  
pp. 1450026 ◽  
Author(s):  
Serkan Karaçuha ◽  
Christian Lomp
Keyword(s):  
Differential Calculus ◽  
Polynomial Algebra ◽  
Exterior Algebra ◽  
Integral Calculus ◽  
De Rham Complex ◽  
Integral Forms ◽  
Rham Complex ◽  
De Rham ◽  
Quantum Polynomial

Hom-connections and associated integral forms have been introduced and studied by Brzeziński as an adjoint version of the usual notion of a connection in non-commutative geometry. Given a flat hom-connection on a differential calculus (Ω, d) over an algebra A yields the integral complex which for various algebras has been shown to be isomorphic to the non-commutative de Rham complex (in the sense of Brzeziński et al. [Non-commutative integral forms and twisted multi-derivations, J. Noncommut. Geom.4 (2010) 281–312]). In this paper we shed further light on the question when the integral and the de Rham complex are isomorphic for an algebra A with a flat Hom-connection. We specialize our study to the case where an n-dimensional differential calculus can be constructed on a quantum exterior algebra over an A-bimodule. Criteria are given for free bimodules with diagonal or upper-triangular bimodule structure. Our results are illustrated for a differential calculus on a multivariate quantum polynomial algebra and for a differential calculus on Manin's quantum n-space.

scholarly journals Chiral de Rham Complex over Locally Complete Intersections

2015 ◽  
Vol 15 (2) ◽  
pp. 353-372
Author(s):  
Fyodor Malikov ◽  
Vadim Schechtman
Keyword(s):  
Complete Intersections ◽  
De Rham Complex ◽  
Rham Complex ◽  
De Rham

scholarly journals A divergent Khintchine theorem in the real, complex, and p-adic fields

2008 ◽  
Vol 48 (2) ◽  
pp. 158-173 ◽  
Author(s):  
V. Bernik ◽  
N. Budarina ◽  
D. Dickinson
Keyword(s):  
The Real ◽  
Real Complex
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