Wahba Problem in SO(3) Dual Algebra

2016 ◽  
Author(s):  
Daniel Condurache ◽  
Adrian Burlacu
Keyword(s):  
Dual Algebra ◽  
Wahba Problem

Duality on the quantum space(3) with two parameters

Open Physics ◽  
2012 ◽  
Vol 10 (5) ◽  
Author(s):  
Muttalip Özavşar ◽  
Gürsel Yeşilot
Keyword(s):  
Hopf Algebra ◽  
Lie Algebra ◽  
Differential Forms ◽  
Quantum Space ◽  
Dual Algebra ◽  
Commutation Relations ◽  
Dual Hopf Algebra ◽  
Invariant Differential ◽  
Leibniz Rules ◽  
Two Parameters

AbstractIn this study, we introduce a dual Hopf algebra in the sense of Sudbery for the quantum space(3) whose coordinates satisfy the commutation relations with two parameters and we show that the dual algebra is isomorphic to the quantum Lie algebra corresponding to the Cartan-Maurer right invariant differential forms on the quantum space(3). We also observe that the quantum Lie algebra generators are commutative as those of the undeformed Lie algebra and the deformation becomes apparent when one studies the Leibniz rules for the generators.

scholarly journals KAPPA-MINKOWSKI SPACETIME, KAPPA-POINCARÉ HOPF ALGEBRA AND REALIZATIONS

2012 ◽  
Vol 09 (06) ◽  
pp. 1261009 ◽  
Author(s):  
DOMAGOJ KOVAČEVIĆ ◽  
STJEPAN MELJANAC
Keyword(s):  
Hopf Algebra ◽  
Star Product ◽  
Minkowski Spacetime ◽  
Inner Product ◽  
Translation Invariance ◽  
Dual Algebra ◽  
Lorentz Algebra ◽  
Heisenberg Algebras ◽  
The Matrix ◽  
Poincaré Algebra

The κ-Minkowski spacetime and Lorentz algebra are unified in unique Lie algebra. Introducing commutative momenta, a family of κ-deformed Heisenberg algebras and κ-deformed Poincaré algebras are defined. They are determined by the matrix depending on momenta. Realizations and star product are defined and analyzed in general. The relation among the coproduct of momenta, realization and the star product is pointed out. Hopf algebra of the Poincaré algebra, related to the covariant realization, is presented in unified covariant form. Left–right dual realizations and dual algebra are introduced and considered. The generalized involution and the star inner product are defined and analyzed. Partial integration and deformed trace property are obtained in general. The translation invariance of the star product is pointed out.

Synthesis of the Pitch Surfaces of Non-Circular Skew-Gears

2010 ◽  
Author(s):  
Giorgio Figliolini ◽  
Pierluigi Rea ◽  
Jorge Angeles
Keyword(s):  
Transmission Ratio ◽  
Dual Algebra ◽  
Cylindrical Gears ◽  
Geometrical Characteristics ◽  
Variable Transmission ◽  
The Subject ◽  
Gear Engagement

The subject of this paper is the synthesis of the pitch surfaces of non-circular skew gears, intended to generate any motion program with a periodically varying transmission ratio. This is done by extending an existing algorithm, which was formulated through the application of dual algebra and the Principle of Transference. In particular, the variable transmission ratio of N-lobed elliptical and logarithmical cylindrical gears is expressed and analyzed along with their main characteristics to test the proposed algorithm, which is implemented in Matlab. The code generates the pitch surfaces of N-lobed elliptical and logarithmical skew gears, along with those of indexing skew gears. Finally, significant numerical and graphical results are shown to analyze the geometrical characteristics of the gear engagement. Not unexpectedly, cylindrical and bevel non-circular gears become particular cases thereof.

scholarly journals Amenability and topological centres of the second duals of Banach algebras

2002 ◽  
Vol 65 (2) ◽  
pp. 191-197 ◽  
Author(s):  
F. Ghahramani ◽  
J. Laali
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Dual Algebra ◽  
Arens Product ◽  
Weak Amenability ◽  
Arens Regularity ◽  
Second Dual

Let  be a Banach algebra and let ** be the second dual algebra of  endowed with the first or the second Arens product. We investigate relations between amenability of ** and Arens regularity of  and the rôle topological centres in amenability of **. We also find conditions under which weak amenability of ** implies weak amenability of .

Synthesis of 4C Mechanism for Generation of a Dual Mathematic Function

2009 ◽  
Vol 15 ◽  
pp. 67-72 ◽  
Author(s):  
I. García-Ríos ◽  
C. Palacios-Montufar ◽  
J.A. Flores Campos ◽  
R. Osorio-Saucedo
Keyword(s):  
Computer Simulation ◽  
Numerical Solution ◽  
Degrees Of Freedom ◽  
Output Function ◽  
Dual Algebra ◽  
Spatial Mechanism ◽  
Dual Number ◽  
Convenient Tool ◽  
Topological Features

In this paper, the synthesis of a spatial mechanism with a 4C topology (four cylindrical joints) to generate a dual mathematic function is presented. The mechanism has two real degrees of freedom (2 DOF) and each of them generates an output function. The dual algebra is used as a convenient tool for solving problems with topological features of this type of mechanisms. The design equations are separated into two parts: the first one is the primary part and the second one corresponds to the dual number. The numerical solution of the equations are given and verified by computer simulation.

scholarly journals Some Examples of Nonassociative Coalgebras and Supercoalgebras

2021 ◽  
Author(s):  
Daniyar Kozybaev ◽  
Ualbai Umirbaev ◽  
Viktor Zhelyabin
Keyword(s):  
Characteristic Zero ◽  
Dual Algebra ◽  
Locally Finite ◽  
Infinite Dimensional ◽  
Lie Coalgebra

Locally finiteness of some varieties of nonassociative coalgebras is studied and the Gelfand-Dorfman construction for Novikov coalgebras and the Kantor construction for Jordan super-coalgebras are given. We give examples of a non-locally finite differential coalgebra, Novikov coalgebra, Lie coalgebra, Jordan super-coalgebra, and right-alternative coalgebra. The dual algebra of each of these examples satisfies very strong additional identities. We also constructed examples of an infinite dimensional simple differential coalgebra, Novikov coalgebra, Lie coalgebra, and Jordan super-coalgebra over a field of characteristic zero.

scholarly journals The Face Semigroup Algebra of a Hyperplane Arrangement

2009 ◽  
Vol 61 (4) ◽  
pp. 904-929 ◽  
Author(s):  
Franco V. Saliola
Keyword(s):  
Algebraic Structure ◽  
Hyperplane Arrangement ◽  
Semigroup Algebra ◽  
Cohomology Algebra ◽  
Koszul Algebra ◽  
Dual Algebra ◽  
Intersection Lattice ◽  
Projective Resolutions ◽  
The Face ◽  
Cartan Invariants

Abstract.This article presents a study of an algebra spanned by the faces of a hyperplane arrangement. The quiver with relations of the algebra is computed and the algebra is shown to be a Koszul algebra. It is shown that the algebra depends only on the intersection lattice of the hyperplane arrangement. A complete systemof primitive orthogonal idempotents for the algebra is constructed and other algebraic structure is determined including: a description of the projective indecomposablemodules, the Cartan invariants, projective resolutions of the simple modules, the Hochschild homology and cohomology, and the Koszul dual algebra. A new cohomology construction on posets is introduced, and it is shown that the face semigroup algebra is isomorphic to the cohomology algebra when this construction is applied to the intersection lattice of the hyperplane arrangement.

Weak Amenability of a Class of Banach Algebras

2001 ◽  
Vol 44 (4) ◽  
pp. 504-508 ◽  
Author(s):  
Yong Zhang
Keyword(s):  
Banach Algebra ◽  
Left Ideal ◽  
Banach Algebras ◽  
Approximate Identity ◽  
Dual Algebra ◽  
Weak Amenability ◽  
Second Dual

AbstractWe show that, if a Banach algebra is a left ideal in its second dual algebra and has a left bounded approximate identity, then the weak amenability of implies the (2m+ 1)-weak amenability of for all m ≥ 1.

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