scholarly journals A FINITE QUANTUM SYMMETRY OF $M(3, {\Bbb C})$

1998 ◽  
Vol 13 (24) ◽  
pp. 4147-4161 ◽  
Author(s):  
LUDWIK DABROWSKI ◽  
FABRIZIO NESTI ◽  
PASQUALE SINISCALCO
Keyword(s):  
Standard Model ◽  
Exact Sequence ◽  
Hopf Algebra ◽  
Quantum Group ◽  
Recent Work ◽  
Quantum Groups ◽  
Matrix Algebra ◽  
Group Symmetry ◽  
The Standard Model ◽  
The Matrix

The 27-dimensional Hopf algebra A(F), defined by the exact sequence of quantum groups [Formula: see text], [Formula: see text], is studied as a finite quantum group symmetry of the matrix algebra [Formula: see text], describing the color sector of Alain Connes' formulation of the Standard Model. The duality with the Hopf algebra ℋ, investigated in a recent work by Robert Coquereaux, is established and used to define a representation of ℋ on [Formula: see text] and two commuting representation of ℋ on A(F).

ON MATRIX QUANTUM GROUPS OF TYPE An

2000 ◽  
Vol 11 (09) ◽  
pp. 1115-1146 ◽  
Author(s):  
HO Hai PHUNG
Keyword(s):  
Hopf Algebra ◽  
Quantum Group ◽  
Quantum Groups ◽  
Semi Group ◽  
The Matrix ◽  
Hecke Symmetry ◽  
Matrix Quantum

Given a Hecke symmetry R, one can define a matrix bialgebra ER and a matrix Hopf algebra HR, which are called function rings on the matrix quantum semi-group and matrix quantum groups associated to R. We show that for an even Hecke symmetry, the rational representations of the corresponding quantum group are absolutely reducible and that the fusion coefficients of simple representations depend only on the rank of the Hecke symmetry. Further we compute the quantum rank of simple representations. We also show that the quantum semi-group is "Zariski" dense in the quantum group. Finally we give a formula for the integral.

scholarly journals Long-distance QCD effects in FCNC B → γl+l- decays

2018 ◽  
Vol 192 ◽  
pp. 00031 ◽  
Author(s):  
Anastasiia Kozachuk ◽  
Dmitri Melikhov ◽  
Nikolai Nikitin
Keyword(s):  
Standard Model ◽  
Recent Work ◽  
Flavour Changing Neutral Currents ◽  
Neutral Currents ◽  
Long Distance ◽  
Leptonic Decays ◽  
The Standard Model

This presentation reviews the main results of our recent work [1] on rare radiative leptonic decays Bd,s → γμ+μ- and Bd,s → γe+e- induced by flavour-changing neutral currents (FCNC) in the Standard Model.

scholarly journals A categorical reconstruction of crystals and quantum groups at q = 0

2019 ◽  
Vol 70 (3) ◽  
pp. 895-925
Author(s):  
Craig Smith
Keyword(s):  
Hopf Algebra ◽  
Quantum Group ◽  
Lie Algebra ◽  
Quantum Groups ◽  
Analogous Result ◽  
Crystal Bases ◽  
Direct Sums ◽  
Finite Dimensional ◽  
Monoidal Structure

Abstract The quantum co-ordinate algebra Aq(g) associated to a Kac–Moody Lie algebra g forms a Hopf algebra whose comodules are direct sums of finite-dimensional irreducible Uq(g) modules. In this paper, we investigate whether an analogous result is true when q=0. We classify crystal bases as coalgebras over a comonadic functor on the category of pointed sets and encode the monoidal structure of crystals into a bicomonadic structure. In doing this, we prove that there is no coalgebra in the category of pointed sets whose comodules are equivalent to crystal bases. We then construct a bialgebra over Z whose based comodules are equivalent to crystals, which we conjecture is linked to Lusztig’s quantum group at v=∞.

scholarly journals A REVIEW OF THE MAGNITUDES OF THE CKM MATRIX ELEMENTS

2008 ◽  
Vol 23 (31) ◽  
pp. 4945-4958 ◽  
Author(s):  
FRANCESCA DI LODOVICO
Keyword(s):  
Standard Model ◽  
Current Status ◽  
Matrix Elements ◽  
Ckm Matrix ◽  
The Standard Model ◽  
The Matrix ◽  
The Absolute ◽  
Ckm Matrix Elements

Flavour mixing is described within the Standard Model by the Cabibbo–Kobayashi–Maskawa (CKM) matrix elements. With the increasingly higher statistics collected by many experiments, the matrix elements are measured with improved precision, allowing for more stringent tests of the Standard Model. In this paper, a review of the current status of the absolute values of the CKM matrix elements is presented, with particular attention to the latest measurements.

scholarly journals The dynamicalU(n)quantum group

2006 ◽  
Vol 2006 ◽  
pp. 1-30 ◽  
Author(s):  
Erik Koelink ◽  
Yvette Van Norden
Keyword(s):  
Quantum Group ◽  
Matrix Algebra ◽  
Exterior Algebra ◽  
Matrix Elements ◽  
Algebra Representation ◽  
The Matrix ◽  
Quantum Minor ◽  
Quantum Determinant

We study the dynamical analogue of the matrix algebraM(n), constructed from a dynamicalR-matrix given by Etingof and Varchenko. A left and a right corepresentation of this algebra, which can be seen as analogues of the exterior algebra representation, are defined and this defines dynamical quantum minor determinants as the matrix elements of these corepresentations. These elements are studied in more detail, especially the action of the comultiplication and Laplace expansions. Using the Laplace expansions we can prove that the dynamical quantum determinant is almost central, and adjoining an inverse the antipode can be defined. This results in the dynamicalGL(n)quantum group associated to the dynamicalR-matrix. We study a∗-structure leading to the dynamicalU(n)quantum group, and we obtain results for the canonical pairing arising from theR-matrix.

scholarly journals THE LEE-WICK STANDARD MODEL

2010 ◽  
Vol 25 (02n03) ◽  
pp. 587-596 ◽  
Author(s):  
MARK B. WISE
Keyword(s):  
Higgs Boson ◽  
Standard Model ◽  
Recent Work ◽  
Boson Mass ◽  
Higgs Boson Mass ◽  
Negative Norm ◽  
Higher Derivative ◽  
The Standard Model ◽  
Higher Derivatives

This article reviews some recent work on a version of the standard model (the Lee-Wick standard model) that contains higher derivative kinetic terms that improve the convergence of loop diagrams removing the quadratic divergence in the Higgs boson mass. Naively higher derivative theories of this type are not acceptable since the higher derivative terms either cause instabilities (from negative energies) or a loss of unitarity (from negative norm states). Lee and Wick provided an interpretation for such theories arguing that theories with higher derivative kinetic terms can be unitary and stable if the states associated with the massive propagator poles, that arise from the higher derivatives, have widths and hence decay and are not in the spectrum of the theory.

Physics potential and motivations for a muon collider

2016 ◽  
Vol 31 (18) ◽  
pp. 1630028 ◽  
Author(s):  
Mario Greco
Keyword(s):  
Higgs Boson ◽  
Standard Model ◽  
Recent Work ◽  
Precise Measurement ◽  
Detailed Knowledge ◽  
Higgs Particle ◽  
Fundamental Component ◽  
Physics Potential ◽  
The Standard Model ◽  
Muon Collider

The discovery of the Higgs particle is demanding a detailed knowledge of the properties of this fundamental component of the Standard Model. From the available data however, it cannot be concluded yet that we have found the SM Higgs boson and not one of the scalars postulated within the possible extensions of the SM. It is shown that a Higgs factory through a muon collider is particularly appropriate for precision studies of the properties of this particle. However sizable QED radiative effects — of order of 50% — must be carefully taken into account for a precise measurement of the leptonic and total widths of the Higgs particle. The results presented here are mainly based on a recent work in collaboration of Tao Han and Zhen Liu.

Understanding the q-Factors in Quantum Group Symmetry

1997 ◽  
Vol 52 (1-2) ◽  
pp. 59-62
Author(s):  
L. C. Biedenharnf ◽  
K. Srinivasa Rao
Keyword(s):  
Characteristic Feature ◽  
Quantum Group ◽  
Quantum Groups ◽  
Group Symmetry ◽  
Explicit Calculation ◽  
Matrix Elements ◽  
Structural Symmetry ◽  
Symmetry Properties ◽  
Q Factors ◽  
Tensor Operators

AbstractA characteristic feature of quantum groups is the occurrence of q-factors (factors of the form qk, k ∈ ℝ), which implement braiding symmetry. We show how the q-factors in matrix elements of elementary q-tensor operators (for all Uq(n)) may be evaluated, without explicit calculation, directly from structural symmetry properties.

scholarly journals BICROSSPRODUCTS OF ALGEBRAIC QUANTUM GROUPS

2013 ◽  
Vol 24 (01) ◽  
pp. 1250131
Author(s):  
L. DELVAUX ◽  
A. VAN DAELE ◽  
S. H. WANG
Keyword(s):  
Hopf Algebra ◽  
Quantum Group ◽  
Quantum Groups ◽  
Smash Product ◽  
Module Algebra ◽  
Algebraic Quantum ◽  
Algebra Theory ◽  
Extra Structure

Let A and B be two algebraic quantum groups. Assume that B is a right A-module algebra and that A is a left B-comodule coalgebra. If the action and coaction are matched, it is possible to define a coproduct Δ# on the smash product A#B making the pair (A#B, Δ#) into an algebraic quantum group. In this paper we study the various data of the bicrossproduct A#B, such as the modular automorphisms, the modular elements, … and we obtain formulas in terms of the data of the components A and B. Secondly, we look at the dual of A#B (in the sense of algebraic quantum groups) and we show it is itself a bicrossproduct (of the second type) of the duals [Formula: see text] and [Formula: see text]. We give some examples that are typical for algebraic quantum groups. In particular, we focus on the extra structure, provided by the integrals and associated objects. It should be mentioned that with examples of bicrossproducts of algebraic quantum groups, we do get examples that are essentially different from those commonly known in Hopf algebra theory.

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