scholarly journals Cohomological invariants of representations of 3-manifold groups

2020 ◽  
pp. 2043003
Author(s):  
Haimiao Chen
Keyword(s):  
Abelian Group ◽  
Discrete Group ◽  
Representation Formula ◽  
Practical Method ◽  
Cohomological Invariants ◽  
Continuous Map ◽  
Definition Of ◽  
Manifolds With Corners ◽  
Chern Simons

Suppose [Formula: see text] is a discrete group, and [Formula: see text], with [Formula: see text] an abelian group. Given a representation [Formula: see text], with [Formula: see text] a closed 3-manifold, put [Formula: see text], where [Formula: see text] is a continuous map inducing [Formula: see text] which is unique up to homotopy, and [Formula: see text] is the pairing. We extend the definition of [Formula: see text] to manifolds with corners, and establish a gluing law. Based on these, we present a practical method for computing [Formula: see text] when [Formula: see text] is given by a surgery along a link [Formula: see text]. In particular, the Chern–Simons invariant can be computed this way.

scholarly journals A lattice-theoretic characterization of pure subgroups of Abelian groups

2021 ◽  
Author(s):  
M. Ferrara ◽  
M. Trombetti
Keyword(s):  
Abelian Group ◽  
Abelian Groups ◽  
Subgroup Lattice ◽  
General Definition ◽  
Short Paper ◽  
Theoretic Characterization ◽  
Definition Of

AbstractLet G be an abelian group. The aim of this short paper is to describe a way to identify pure subgroups H of G by looking only at how the subgroup lattice $$\mathcal {L}(H)$$ L ( H ) embeds in $$\mathcal {L}(G)$$ L ( G ) . It is worth noticing that all results are carried out in a local nilpotent context for a general definition of purity.

scholarly journals Moving Heat Source Reconstruction from Cauchy Boundary Data: The Cartesian Coordinates Case

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
Nilson C. Roberty ◽  
Denis M. de Sousa ◽  
Marcelo L. S. Rainha
Keyword(s):  
Helmholtz Equation ◽  
Boundary Data ◽  
Representation Formula ◽  
Transient Heat Conduction ◽  
Thermal Source ◽  
Source Reconstruction ◽  
Modified Helmholtz Equation ◽  
Time Space ◽  
Definition Of ◽  
Characteristic Interval

We consider the problem of reconstruction of an unknown characteristic interval and block transient thermal source inside a domain. By exploring the definition of an Extended Dirichlet to Neumann map in the time space cylinder that has been introduced in Roberty and Rainha (2010a), we can treat the problem with methods similar to that used in the analysis of the stationary source reconstruction problem. Further, the finite differenceθ-scheme applied to the transient heat conduction equation leads to a model based on a sequence of modified Helmholtz equation solutions. For each modified Helmholtz equation the characteristic interval and parallelepiped source function may be reconstructed uniquely from the Cauchy boundary data. Using representation formula we establish reciprocity functional mapping functions that are solutions of the modified Helmholtz equation to their integral in the unknown characteristic support. Numerical experiment for capture of an interval and an rectangular parallelepiped characteristic source inside a cubic box domain from boundary data are presented in threedimensional and one-dimensional implementations. The problem of centroid determination is addressed and questions are discussed from an computational points of view.

scholarly journals Quasi-flat representations of uniform groups and quantum groups

2019 ◽  
Vol 18 (08) ◽  
pp. 1950155 ◽  
Author(s):  
Teodor Banica ◽  
Alexandru Chirvasitu
Keyword(s):  
Quantum Groups ◽  
Discrete Group ◽  
Homogeneous Spaces ◽  
Model Space ◽  
Representation Formula ◽  
Discrete Groups ◽  
Universal Model ◽  
Induced Representation ◽  
Negative Results ◽  
Number Formula

Given a discrete group [Formula: see text] and a number [Formula: see text], a unitary representation [Formula: see text] is called quasi-flat when the eigenvalues of each [Formula: see text] are uniformly distributed among the [Formula: see text]th roots of unity. The quasi-flat representations of [Formula: see text] form altogether a parametric matrix model [Formula: see text]. We compute here the universal model space [Formula: see text] for various classes of discrete groups, notably with results in the case where [Formula: see text] is metabelian. We are particularly interested in the case where [Formula: see text] is a union of compact homogeneous spaces, and where the induced representation [Formula: see text] is stationary in the sense that it commutes with the Haar functionals. We present several positive and negative results on this subject. We also discuss similar questions for the discrete quantum groups, proving a stationarity result for the discrete dual of the twisted orthogonal group [Formula: see text].

scholarly journals A Generalization of Final Rank of Primary Abelian Groups

1970 ◽  
Vol 22 (6) ◽  
pp. 1118-1122 ◽  
Author(s):  
Doyle O. Cutler ◽  
Paul F. Dubois
Keyword(s):  
Abelian Group ◽  
Abelian Groups ◽  
Basic Subgroup ◽  
Primary Abelian Group ◽  
Limit Ordinal ◽  
Final Rank ◽  
Definition Of ◽  
Group Recall

Let G be a p-primary Abelian group. Recall that the final rank of G is infn∈ω{r(pnG)}, where r(pnG) is the rank of pnG and ω is the first limit ordinal. Alternately, if Γ is the set of all basic subgroups of G, we may define the final rank of G by supB∈Γ {r(G/B)}. In fact, it is known that there exists a basic subgroup B of G such that r(G/B) is equal to the final rank of G. Since the final rank of G is equal to the final rank of a high subgroup of G plus the rank of pωG, one could obtain the same information if the definition of final rank were restricted to the class of p-primary Abelian groups of length ω.

Reliability Analysis of Cracking and Faulting Prediction in the New Mechanistic–Empirical Pavement Design Procedure

2005 ◽  
Vol 1936 (1) ◽  
pp. 150-160 ◽  
Author(s):  
Michael Darter ◽  
Lev Khazanovich ◽  
Tom Yu ◽  
Jag Mallela
Keyword(s):  
Monte Carlo ◽  
Reliability Analysis ◽  
Design Procedure ◽  
Practical Method ◽  
Pavement Design ◽  
Rigid Pavement ◽  
Pavement Distress ◽  
Reliability Based Design ◽  
Definition Of ◽  
Reliability Performance

Reliability analysis is an important part of the mechanistic–empirical pavement design guide (M-E PDG). Even though mechanistic concepts provide a more accurate and realistic methodology for pavement design, a practical method to consider the uncertainties and variations in design and construction is needed so that a new or rehabilitated pavement can be designed for a desired level of reliability (performance as designed). Several methods, ranging from closed-form approaches to simulation-based methods, can be adopted to perform reliability-based design. However, some methods may be more suitable than others, given the complexities of the design procedure. A formal definition of reliability within the context of the M-E PDG, as well as two reliability analysis approaches considered for incorporation into the design procedure for evaluating the reliability of the rigid pavement design for cracking and faulting, was evaluated. A Monte Carlo–based simulation was combined with the damage accumulation procedure for rigid pavement distress prediction. This approach is recommended for future improvements of the procedure. The development of the reliability analysis procedure implemented into the M-E PDG also was documented. It was demonstrated that although the adopted approach is not as sophisticated as a Monte Carlo–based one, it still represents a step forward compared with AASHTO-93 reliability analysis.

scholarly journals FERMIONS FROM PHOTONS: BOSONIZATION OF QED IN 2+1 DIMENSIONS

1994 ◽  
Vol 09 (27) ◽  
pp. 4669-4700 ◽  
Author(s):  
A. KOVNER ◽  
P.S. KURZEPA
Keyword(s):  
Perturbation Theory ◽  
Vector Potential ◽  
Energy Momentum Tensor ◽  
Lorentz Invariance ◽  
Hamiltonian Formalism ◽  
Momentum Tensor ◽  
Regularization Procedure ◽  
Local Polynomial ◽  
Definition Of ◽  
Chern Simons

We perform the complete bosonization of (2+1)-dimensional QED with one fermionic flavor in the Hamiltonian formalism. The Fermi operators are explicitly constructed in terms of the vector potential and the electric field. We carefully specify the regularization procedure involved in the definition of these operators, and calculate the fermionic bilinears and the energy-momentum tensor. The algebra of bilinears exhibits the Schwinger terms which also appear in perturbation theory. The bosonic Hamiltonian is a local, polynomial functional of Ai and Ei, and we check explicitly the Lorentz invariance of the resulting bosonic theory. Our construction is conceptually very similar to Mandelstam’s construction in 1+1 dimensions, and is dissimilar from the recent bosonization attempts in 2+1 dimensions, which hinge crucially on the presence of a Chern-Simons term.

ANYON EQUATION ON A TORUS

1992 ◽  
Vol 07 (23) ◽  
pp. 5797-5831 ◽  
Author(s):  
CHOON-LIN HO ◽  
YUTAKA HOSOTANI
Keyword(s):  
Field Theory ◽  
Wave Function ◽  
Essential Role ◽  
Wilson Line ◽  
Regular Function ◽  
Gauge Fields ◽  
Quantum Field ◽  
Many Body ◽  
Definition Of ◽  
Chern Simons

Starting from the quantum field theory of nonrelativistic matter on a torus interacting with Chern-Simons gauge fields, we derive the Schrödinger equation for an anyon system. The nonintegrable phases of the Wilson line integrals on a torus play an essential role. In addition to generating degenerate vacua, they enter in the definition of a many-body Schrödinger wave function in quantum mechanics, which can be defined as a regular function of the coordinates of anyons. It obeys a non-Abelian representation of the braid group algebra, being related to Einarsson’s wave function by a singular gauge transformation.

scholarly journals Note on the semi-simplicity of measure algebras

2019 ◽  
Vol 192 (4) ◽  
pp. 935-938
Author(s):  
László Székelyhidi
Keyword(s):  
Abelian Group ◽  
Compact Abelian Group ◽  
Discrete Group ◽  
Locally Compact Abelian Group ◽  
Measure Algebra ◽  
Locally Compact ◽  
Group Case

AbstractIn this paper we prove that the measure algebra of a locally compact abelian group is semi-simple. This result extends the corresponding result of S. A. Amitsur in the discrete group case using a completely different approach.

On a special single-power cyclic hypergroup and its automorphisms

2016 ◽  
Vol 08 (04) ◽  
pp. 1650059 ◽  
Author(s):  
M. Al Tahan ◽  
B. Davvaz
Keyword(s):  
Abelian Group ◽  
Braid Group ◽  
Definition Of ◽  
Single Power

After introducing the definition of hypergroups by Marty, the study of hyperstructures and its applications has been of great importance. In this paper, we find a link between hyperstructures and the infinite non-abelian group, braid group [Formula: see text]. This is the first connection to be done between these two different domains. First, we define a new hyperoperation ⋆ associated to [Formula: see text] and study its properties. Next, we prove that [Formula: see text] is a single-power cyclic hypergroup with infinite period. Then, we define an onto homomorphism from [Formula: see text] to another hypergroup. Finally, we determine the set of all automorphisms of [Formula: see text] and prove that it is a group under the operation of functions composition.

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