MOMENTUM MAPPINGS AND POISSON COHOMOLOGY

1996 ◽  
Vol 07 (03) ◽  
pp. 329-358 ◽  
Author(s):  
VIKTOR L. GINZBURG
Keyword(s):  
Poisson Structure ◽  
Poisson Manifold ◽  
Existence Problem ◽  
Necessary And Sufficient Condition ◽  
Momentum Mapping ◽  
Lie Algebra Cohomology ◽  
Poisson Cohomology ◽  
Poisson Actions ◽  
Poisson Lie Groups ◽  
Necessary And Sufficient

We analyze the question of existence and uniqueness of equivariant momentum mappings for Poisson actions of Poisson Lie groups. A necessary and sufficient condition for the equivariant momentum mapping to be unique is given. The existence problem is solved under some extra hypotheses, for example, when the action preserves the Poisson structure. In this case, the problem is closely related to the triviality of the induced group action on the Poisson cohomology. This action is shown to be trivial whenever the group is compact or semisimple. Conceptually, these results rely upon a version of “Poisson calculus” developed here to make one-forms on a Poisson manifold induce a “flow” preserving the Poisson structure. In the general case, obstructions to the existence of an infinitesimal version of an equivariant momentum mapping are found. Using Lie algebra cohomology with coefficients in Fréchet modules, we show that the obstructions vanish, and the infinitesimal mapping exists, when the group is compact semisimple. We also prove the rigidity of compact group actions preserving the Poisson structure on a compact manifold and calculate the Poisson cohomology of the Poisson homogeneous space [Formula: see text].

scholarly journals Algebraic Structure of Holomorphic Poisson Cohomology on Nilmanifolds

2019 ◽  
Vol 6 (1) ◽  
pp. 88-102
Author(s):  
Yat Sun Poon ◽  
John Simanyi
Keyword(s):  
Poisson Structure ◽  
Algebraic Structure ◽  
Complex Structure ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Poisson Cohomology ◽  
Abelian Complex Structure ◽  
Gerstenhaber Algebras ◽  
Holomorphic Poisson Cohomology ◽  
Necessary And Sufficient

AbstractIt is proved that on nilmanifolds with abelian complex structure, there exists a canonically constructed non-trivial holomorphic Poisson structure.We identify the necessary and sufficient condition for its associated cohomology to be isomorphic to the cohomology associated to trivial (zero) holomorphic Poisson structure. We also identify a sufficient condition for this isomorphism to be at the level of Gerstenhaber algebras.

EQUIVARIANT POISSON COHOMOLOGY AND A SPECTRAL SEQUENCE ASSOCIATED WITH A MOMENT MAP

1999 ◽  
Vol 10 (08) ◽  
pp. 977-1010 ◽  
Author(s):  
VIKTOR L. GINZBURG
Keyword(s):  
Tensor Product ◽  
Spectral Sequence ◽  
Vector Fields ◽  
Equivariant Cohomology ◽  
Poisson Manifold ◽  
Momentum Mapping ◽  
Poisson Cohomology ◽  
Leray Spectral Sequence ◽  
Differential Complex ◽  
Extensive Introduction

We introduce and study a new spectral sequence associated with a Poisson group action on a Poisson manifold and an equivariant momentum mapping. This spectral sequence is a Poisson analog of the Leray spectral sequence of a fibration. The spectral sequence converges to the Poisson cohomology of the manifold and has the E2-term equal to the tensor product of the cohomology of the Lie algebra and the equivariant Poisson cohomology of the manifold. The latter is defined as the equivariant cohomology of the multi-vector fields made into a G-differential complex by means of the momentum mapping. An extensive introduction to equivariant cohomology of G-differential complexes is given including some new results and a number of examples and applications are considered.

Moduli Space of Flat Connections as a Poisson Manifold

1997 ◽  
Vol 11 (26n27) ◽  
pp. 3195-3206 ◽  
Author(s):  
V. V. Fock ◽  
A. A. Rosly
Keyword(s):  
Riemann Surface ◽  
Lie Groups ◽  
Poisson Structure ◽  
Moduli Space ◽  
Poisson Manifold ◽  
Gauge Fields ◽  
Two Dimensional ◽  
Flat Connections ◽  
Lattice Gauge ◽  
Poisson Lie Groups

In this talk we describe the Poisson structure of the moduli space of flat connections on a two dimensional Riemann surface in terms of lattice gauge fields and Poisson–Lie groups.

scholarly journals Extensions and automorphisms of Lie algebras

2016 ◽  
Vol 16 (09) ◽  
pp. 1750162 ◽  
Author(s):  
Valeriy G. Bardakov ◽  
Mahender Singh
Keyword(s):  
Exact Sequence ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Short Exact Sequence ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Nilpotent Lie Algebra ◽  
Lie Algebra Cohomology ◽  
Cohomology Of Lie Algebras ◽  
Necessary And Sufficient

Let [Formula: see text] be a short exact sequence of Lie algebras over a field [Formula: see text], where [Formula: see text] is abelian. We show that the obstruction for a pair of automorphisms in [Formula: see text] to be induced by an automorphism in [Formula: see text] lies in the Lie algebra cohomology [Formula: see text]. As a consequence, we obtain a four term exact sequence relating automorphisms, derivations and cohomology of Lie algebras. We also obtain a more explicit necessary and sufficient condition for a pair of automorphisms in [Formula: see text] to be induced by an automorphism in [Formula: see text], where [Formula: see text] is a free nilpotent Lie algebra of rank [Formula: see text] and step [Formula: see text].

A Proposed Framework Emphasizing Auditor Reliability over Auditor Independence

2003 ◽  
Vol 17 (3) ◽  
pp. 257-266 ◽  
Author(s):  
Mark H. Taylor ◽  
F. Todd DeZoort ◽  
Edward Munn ◽  
Martha Wetterhall Thomas
Keyword(s):  
Public Interest ◽  
Auditor Independence ◽  
Public Confidence ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Accounting Profession ◽  
The Public ◽  
Necessary And Sufficient

This paper introduces an auditor reliability framework that repositions the role of auditor independence in the accounting profession. The framework is motivated in part by widespread confusion about independence and the auditing profession's continuing problems with managing independence and inspiring public confidence. We use philosophical, theoretical, and professional arguments to argue that the public interest will be best served by reprioritizing professional and ethical objectives to establish reliability in fact and appearance as the cornerstone of the profession, rather than relationship-based independence in fact and appearance. This revised framework requires three foundation elements to control subjectivity in auditors' judgments and decisions: independence, integrity, and expertise. Each element is a necessary but not sufficient condition for maximizing objectivity. Objectivity, in turn, is a necessary and sufficient condition for achieving and maintaining reliability in fact and appearance.

The Power of Public Positions

2018 ◽  
Author(s):  
Thomas Sinclair
Keyword(s):  
Detailed Analysis ◽  
Political Authority ◽  
The State ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
State Institutions ◽  
State Of Nature ◽  
Necessary And Sufficient

The Kantian account of political authority holds that the state is a necessary and sufficient condition of our freedom. We cannot be free outside the state, Kantians argue, because any attempt to have the “acquired rights” necessary for our freedom implicates us in objectionable relations of dependence on private judgment. Only in the state can this problem be overcome. But it is not clear how mere institutions could make the necessary difference, and contemporary Kantians have not offered compelling explanations. A detailed analysis is presented of the problems Kantians identify with the state of nature and the objections they face in claiming that the state overcomes them. A response is sketched on behalf of Kantians. The key idea is that under state institutions, a person can make claims of acquired right without presupposing that she is by nature exceptional in her capacity to bind others.

Interest rate option hedging portfolios without bank account

2019 ◽  
Vol 37 (1) ◽  
pp. 134-142
Author(s):  
Alberto Bueno-Guerrero
Keyword(s):  
Design Methodology ◽  
Contingent Claim ◽  
Necessary And Sufficient Condition ◽  
Barrier Option ◽  
Bank Account ◽  
Content Type ◽  
Option Hedging ◽  
Hedging Portfolio ◽  
Necessary And Sufficient ◽  
First Time

Purpose This paper aims to study the conditions for the hedging portfolio of any contingent claim on bonds to have no bank account part. Design/methodology/approach Hedging and Malliavin calculus techniques recently developed under a stochastic string framework are applied. Findings A necessary and sufficient condition for the hedging portfolio to have no bank account part is found. This condition is applied to a barrier option, and an example of a contingent claim whose hedging portfolio has a bank account part different from zero is provided. Originality/value To the best of the authors’ knowledge, this is the first time that this issue has been addressed in the literature.

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