scholarly journals Secondary characteristic class of Lie algebra extensions

2019 ◽  
Vol 147 (3) ◽  
pp. 443-453
Author(s):  
Stefan WAGNER
Keyword(s):  
Lie Algebra ◽  
Characteristic Class ◽  
Secondary Characteristic

ON THE FIRST MORITA-MUMFORD CLASS OF SURFACE BUNDLES OVER S1 AND THE ROCHLIN INVARIANT

2000 ◽  
Vol 09 (02) ◽  
pp. 179-186 ◽  
Author(s):  
TERUAKI KITANO
Keyword(s):  
Characteristic Class ◽  
Bounded Cohomology ◽  
Spin Structures ◽  
Surface Bundles ◽  
Secondary Characteristic ◽  
Class E

We consider the first Morita-Mumford class e1 of surface bundles over S1 as a bounded cohomology over Z. It is trivial in general. However in some class of surface bundles over S1 with spin structures, [Formula: see text] makes sense as a characteristic class of them and it is just the Rochlin invariant of such a 3-manifold. It gives a description of the Rochlin invariant as a secondary characteristic class.

scholarly journals ON THE GENERALIZED VOLUME CONJECTURE AND REGULATOR

2008 ◽  
Vol 10 (supp01) ◽  
pp. 1023-1032 ◽  
Author(s):  
WEIPING LI ◽  
QINGXUE WANG
Keyword(s):  
Line Bundle ◽  
Chern Class ◽  
Quantization Condition ◽  
Character Variety ◽  
Characteristic Class ◽  
Volume Conjecture ◽  
Smooth Part ◽  
First Chern Class ◽  
Chern Simons ◽  
Secondary Characteristic

In this paper, by using the regulator map of Beilinson-Deligne on a curve, we show that the quantization condition posed by Gukov is true for the SL2(ℂ) character variety of the hyperbolic knot in S3. Furthermore, we prove that the corresponding ℂ*-valued closed 1-form is a secondary characteristic class (Chern-Simons) arising from the vanishing first Chern class of the flat line bundle over the smooth part of the character variety, where the flat line bundle is the pullback of the universal Heisenberg line bundle over ℂ* × ℂ*. Based on this result, we give a reformulation of Gukov's generalized volume conjecture from a motivic perspective.

Integrable two-dimensional dynamical systems and the characteristic Lie algebras

2007 ◽  
Vol 5 ◽  
pp. 195-200
Author(s):  
A.V. Zhiber ◽  
O.S. Kostrigina
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Second Order ◽  
System Of Equations ◽  
Two Dimensional ◽  
Finite Dimensional ◽  
Dimensional Dynamical System

In the paper it is shown that the two-dimensional dynamical system of equations is Darboux integrable if and only if its characteristic Lie algebra is finite-dimensional. The class of systems having a full set of fist and second order integrals is described.

Reduction of partially invariant submodels of rank 3 defect 1 to invariant submodels

2018 ◽  
Vol 13 (3) ◽  
pp. 59-63 ◽  
Author(s):  
D.T. Siraeva
Keyword(s):  
Equation Of State ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Gas Dynamics ◽  
Hydrodynamic Type ◽  
System Of Equations ◽  
Two Dimensional ◽  
Equations Of Gas Dynamics ◽  
Entropy Functions

Equations of hydrodynamic type with the equation of state in the form of pressure separated into a sum of density and entropy functions are considered. Such a system of equations admits a twelve-dimensional Lie algebra. In the case of the equation of state of the general form, the equations of gas dynamics admit an eleven-dimensional Lie algebra. For both Lie algebras the optimal systems of non-similar subalgebras are constructed. In this paper two partially invariant submodels of rank 3 defect 1 are constructed for two-dimensional subalgebras of the twelve-dimensional Lie algebra. The reduction of the constructed submodels to invariant submodels of eleven-dimensional and twelve-dimensional Lie algebras is proved.

ε‎-Invariance

2018 ◽  
Author(s):  
Ercüment H. Ortaçgil
Keyword(s):  
Lie Algebra ◽  
Lie Group

The discussions up to Chapter 4 have been concerned with the Lie group. In this chapter, the Lie algebra is constructed by defining the operators ∇ and ∇̃.

ANTI-SELF-DUAL SOLUTIONS OF THE YANG-MILLS EQUATIONS IN 4n DIMENSIONS

1992 ◽  
Vol 07 (23) ◽  
pp. 2077-2085 ◽  
Author(s):  
A. D. POPOV
Keyword(s):  
Scalar Field ◽  
Euclidean Space ◽  
Lie Algebra ◽  
Linear Equations ◽  
Dual Solutions ◽  
Gauge Fields ◽  
System Of Equations ◽  
Semisimple Lie Algebra ◽  
Yang Mills ◽  
Self Duality

The anti-self-duality equations for gauge fields in d = 4 and a generalization of these equations to dimension d = 4n are considered. For gauge fields with values in an arbitrary semisimple Lie algebra [Formula: see text] we introduce the ansatz which reduces the anti-self-duality equations in the Euclidean space ℝ4n to a system of equations breaking up into the well known Nahm's equations and some linear equations for scalar field φ.

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