scholarly journals Quadratic algebra structure in the 5D Kepler system with non-central potentials and Yang–Coulomb monopole interaction

2017 ◽  
Vol 380 ◽  
pp. 121-134 ◽  
Author(s):  
Md Fazlul Hoque ◽  
Ian Marquette ◽  
Yao-Zhong Zhang
Keyword(s):  
Quadratic Algebra ◽  
Algebra Structure ◽  
Kepler System

scholarly journals GENERALIZED DEFORMED su(2) ALGEBRAS, DEFORMED PARAFERMIONIC OSCILLATORS AND FINITE W-ALGEBRAS

1995 ◽  
Vol 10 (29) ◽  
pp. 2197-2211 ◽  
Author(s):  
D. BONATSOS ◽  
P. KOLOKOTRONIS ◽  
C. DASKALOYANNIS
Keyword(s):  
Representation Theory ◽  
Two Dimensions ◽  
Quadratic Algebra ◽  
Two Dimensional ◽  
Identical Particles ◽  
Mathematical Structures ◽  
Curved Space ◽  
Physical Systems ◽  
Kepler System

Several physical systems (two identical particles in two dimensions, isotropic oscillator and Kepler system in a two-dimensional curved space) and mathematical structures (quadratic algebra QH(3), finite W-algebra [Formula: see text]) are shown to possess the structure of a generalized deformed su (2) algebra, the representation theory of which is known. Furthermore, the generalized deformed parafermionic oscillator is identified with the algebra of several physical systems (isotropic oscillator and Kepler system in two-dimensional curved space, Fokas-Lagerstrom, Smorodinsky-Winternitz and Holt potentials) and mathematical constructions (generalized deformed su (2) algebra, finite W-algebras [Formula: see text] and [Formula: see text]). The fact that the Holt potential is characterized by the [Formula: see text] symmetry is obtained as a by-product.

Thermal-mixture Kepler system in stochastic mechanics

1991 ◽  
Vol 44 (10) ◽  
pp. 6313-6319 ◽  
Author(s):  
Tetsuya Misawa
Keyword(s):  
Stochastic Mechanics ◽  
Kepler System

scholarly journals Blackbox computation of A ∞-algebras

2010 ◽  
Vol 17 (2) ◽  
pp. 391-404
Author(s):  
Mikael Vejdemo-Johansson
Keyword(s):  
Homology Theory ◽  
Algebra Structure ◽  
Finite Amount ◽  
Computational Work ◽  
Dg Algebra ◽  
Dg Algebras

Abstract Kadeishvili's proof of theminimality theorem [T. Kadeishvili, On the homology theory of fiber spaces, Russ. Math. Surv. 35:3 (1980), 231–238] induces an algorithm for the inductive computation of an A ∞-algebra structure on the homology of a dg-algebra. In this paper, we prove that for one class of dg-algebras, the resulting computation will generate a complete A ∞-algebra structure after a finite amount of computational work.

scholarly journals Compact linear operators from an algebraic standpoint

1967 ◽  
Vol 8 (1) ◽  
pp. 41-49 ◽  
Author(s):  
F. F. Bonsall
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Linear Operators ◽  
Identity Operator ◽  
Algebra Structure ◽  
Natural Setting ◽  
Norm Topology ◽  
Bounded Linear ◽  
Underlying Space ◽  
Closed Subalgebra

Let B(X) denote the Banach algebra of all bounded linear operators on a Banach space X. Let t be an element of B(X), and let edenote the identity operator on X. Since the earliest days of the theory of Banach algebras, ithas been understood that the natural setting within which to study spectral properties of t is the Banach algebra B(X), or perhaps a closed subalgebra of B(X) containing t and e. The effective application of this method to a given class of operators depends upon first translating the data into terms involving only the Banach algebra structure of B(X) without reference to the underlying space X. In particular, the appropriate topology is the norm topology in B(X) given by the usual operator norm. Theorem 1 carries out this translation for the class of compact operators t. It is proved that if t is compact, then multiplication by t is a compact linear operator on the closed subalgebra of B(X) consisting of operators that commute with t.

scholarly journals Dual Creation Operators and a Dendriform Algebra Structure on the Quasisymmetric Functions

2017 ◽  
Vol 69 (1) ◽  
pp. 21-53 ◽  
Author(s):  
Darij Grinberg
Keyword(s):  
Hopf Algebras ◽  
Young Tableau ◽  
Vertex Operators ◽  
Schur Function ◽  
Algebra Structure ◽  
Quasisymmetric Functions ◽  
Combinatorial Hopf Algebras ◽  
Dendriform Algebra ◽  
Natural Analogues ◽  
Creation Operators

AbstractThe dual immaculate functions are a basis of the ring QSym of quasisymmetric functions and form one of the most natural analogues of the Schur functions. The dual immaculate function corresponding to a composition is a weighted generating function for immaculate tableaux in the same way as a Schur function is for semistandard Young tableaux; an immaculate tableau is defined similarly to a semistandard Young tableau, but the shape is a composition rather than a partition, and only the first column is required to strictly increase (whereas the other columns can be arbitrary, but each row has to weakly increase). Dual immaculate functions were introduced by Berg, Bergeron, Saliola, Serrano, and Zabrocki in arXiv:1208.5191, and have since been found to possess numerous nontrivial properties.In this note, we prove a conjecture of M. Zabrocki that provides an alternative construction for the dual immaculate functions in terms of certain “vertex operators”. The proof uses a dendriform structure on the ring QSym; we discuss the relation of this structure to known dendriformstructures on the combinatorial Hopf algebras FQSym andWQSym.

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