scholarly journals Representations on partially holomorphic cohomology spaces, revisited

2018 ◽  
pp. 253-303
Author(s):  
Joseph Wolf
Keyword(s):  
Cohomology Spaces

Relative cohomology spaces for some osp(n|2)-modules

2018 ◽  
Vol 59 (10) ◽  
pp. 101704
Author(s):  
Didier Arnal ◽  
Mabrouk Ben Ammar ◽  
Wafa Mtaouaa ◽  
Zeineb Selmi
Keyword(s):  
Relative Cohomology ◽  
Cohomology Spaces

On Harmonic Theory in Flows

2003 ◽  
Vol 46 (4) ◽  
pp. 617-631 ◽  
Author(s):  
Hong Kyung Pak
Keyword(s):  
Contact Manifold ◽  
Natural Generalization ◽  
Basic Flow ◽  
Compact Manifolds ◽  
Cohomology Spaces ◽  
Special Case

AbstractRecently [8], a harmonic theory was developed for a compact contact manifold from the viewpoint of the transversal geometry of contact flow. A contact flow is a typical example of geodesible flow. As a natural generalization of the contact flow, the present paper develops a harmonic theory for various flows on compact manifolds. We introduce the notions of H-harmonic and H*-harmonic spaces associated to a Hörmander flow. We also introduce the notions of basic harmonic spaces associated to a weak basic flow. One of our main results is to show that in the special case of isometric flow these harmonic spaces are isomorphic to the cohomology spaces of certain complexes. Moreover, we find an obstruction for a geodesible flow to be isometric.

Some New Results on L2 Cohomology of Negatively Curved Riemannian Manifolds

2005 ◽  
Vol 57 (2) ◽  
pp. 251-266
Author(s):  
M. Cocos
Keyword(s):  
Heat Equation ◽  
Riemannian Manifolds ◽  
Curved Manifolds ◽  
Negatively Curved ◽  
Regularity Properties ◽  
L2 Cohomology ◽  
Cohomology Spaces

AbstractThe present paper is concerned with the study of the L2 cohomology spaces of negatively curved manifolds. The first half presents a finiteness and vanishing result obtained under some curvature assumptions, while the second half identifies a class of metrics having non-trivial L2 cohomology for degree equal to the half dimension of the space. For the second part we rely on the existence and regularity properties of the solution for the heat equation for forms.

Cohomology spaces of low dimensional complex associative algebras

2017 ◽  
Author(s):  
Nadia F. Mohammed ◽  
Isamiddin S. Rakhimov ◽  
Sharifah Kartini Said Hussain
Keyword(s):  
Associative Algebras ◽  
Low Dimensional ◽  
Cohomology Spaces

The affine cohomology spaces and its applications

2016 ◽  
Vol 13 (02) ◽  
pp. 1650016 ◽  
Author(s):  
Nizar Ben Fraj ◽  
Ismail Laraiedh
Keyword(s):  
Large Class ◽  
Differential Operators ◽  
Lie Superalgebra ◽  
Invariant Differential Operators ◽  
Linear Differential Operators ◽  
Relative Cohomology ◽  
Linear Formula ◽  
Invariant Differential ◽  
Linear Differential ◽  
Cohomology Spaces

We compute the [Formula: see text] cohomology space of the affine Lie superalgebra [Formula: see text] on the (1,1)-dimensional real superspace with coefficient in a large class of [Formula: see text]-modules [Formula: see text]. We apply our results to the module of weight densities and the module of linear differential operators acting on a superspace of weighted densities. This work is the generalization of a result by Basdouri et al. [The linear [Formula: see text]-invariant differential operators on weighted densities on the superspace [Formula: see text] and [Formula: see text]-relative cohomology, Int. J. Geom. Meth. Mod. Phys. 10 (2013), Article ID: 1320004, 9 pp.]

scholarly journals Comodule algebras and 2-cocycles over the (Braided) Drinfeld double

2019 ◽  
Vol 21 (04) ◽  
pp. 1850045 ◽  
Author(s):  
Robert Laugwitz
Keyword(s):  
Hopf Algebra ◽  
Hopf Algebras ◽  
Monoidal Category ◽  
Crossed Product ◽  
Braided Monoidal Category ◽  
Drinfeld Double ◽  
Comodule Algebra ◽  
Category Of Modules ◽  
Cohomology Spaces ◽  
Quasitriangular Hopf Algebra

We show that for dually paired bialgebras, every comodule algebra over one of the paired bialgebras gives a comodule algebra over their Drinfeld double via a crossed product construction. These constructions generalize to working with bialgebra objects in a braided monoidal category of modules over a quasitriangular Hopf algebra. Hence two ways to provide comodule algebras over the braided Drinfeld double (the double bosonization) are provided. Furthermore, a map of second Hopf algebra cohomology spaces is constructed. It takes a pair of 2-cocycles over dually paired Hopf algebras and produces a 2-cocycle over their Drinfeld double. This construction also has an analogue for braided Drinfeld doubles.

Holomorphic and abstract inducing

1984 ◽  
Vol 96 (3) ◽  
pp. 453-468 ◽  
Author(s):  
K. C. Hannabuss
Keyword(s):  
Hilbert Spaces ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Spaces ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact ◽  
Induced Representations ◽  
Projective Representations ◽  
Kernel Hilbert Spaces ◽  
Cohomology Spaces

AbstractA method of constructing projective representations of separable locally compact groups in reproducing kernel Hilbert spaces is presented, based on the generalized inducing process of Rieffel and Fell. Examples show that the method can be used to construct some well-known holomorphically induced representations. Some representations on cohomology spaces are also described.

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