scholarly journals GENERALIZED CONFORMAL SYMMETRY AND EXTENDED OBJECTS FROM THE FREE PARTICLE

1998 ◽  
Vol 13 (28) ◽  
pp. 4889-4911 ◽  
Author(s):  
M. CALIXTO ◽  
V. ALDAYA ◽  
J. GUERRERO
Keyword(s):  
Symplectic Group ◽  
Conformal Symmetry ◽  
Free Particle ◽  
Wave Functions ◽  
Degree Of Freedom ◽  
Quadratic Functions ◽  
Dimensional Algebra ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Internal Character

The algebra of linear and quadratic functions of basic observables on the phase space of either the free particle or the harmonic oscillator possesses a finite-dimensional anomaly. The quantization of these systems outside the critical values of the anomaly leads to a new degree of freedom which shares its internal character with spin, but nevertheless features an infinite number of different states. Both are associated with the transformation properties of wave functions under the Weyl-symplectic group [Formula: see text]. The physical meaning of this new degree of freedom can be established, with a major scope, only by analyzing the quantization of an infinite-dimensional algebra of diffeomorphisms generalizing string symmetry and leading to more general extended objects.

scholarly journals Higher Spin Symmetries of the Free Schrödinger Equation

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Mauricio Valenzuela
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Free Particle ◽  
Symmetry Algebra ◽  
Dimensional Algebra ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Spatial Dimensions ◽  
Higher Spin ◽  
Symmetry Generators

It is shown that the Schrödinger symmetry algebra of a free particle indspatial dimensions can be embedded into a representation of the higher spin algebra. The latter spans an infinite dimensional algebra of higher-order symmetry generators of the free Schrödinger equation. An explicit representation of the maximal finite dimensional subalgebra of the higher spin algebra is given in terms of nonrelativistic generators. We show also how to convert Vasiliev’s equations into an explicit nonrelativistic covariant form, such that they might apply to nonrelativistic systems. Our procedure reveals that the space of solutions of the Schrödinger equation can be regarded also as a supersymmetric module.

scholarly journals COHOMOLOGY RING OF THE BRST OPERATOR ASSOCIATED TO THE SUM OF TWO PURE SPINORS

2013 ◽  
Vol 28 (23) ◽  
pp. 1350107 ◽  
Author(s):  
ANDREI MIKHAILOV ◽  
ALBERT SCHWARZ ◽  
RENJUN XU
Keyword(s):  
Cohomology Ring ◽  
Type Ii ◽  
Pure Spinor ◽  
Multiplicative Structure ◽  
Dimensional Algebra ◽  
Dimensional Vector Space ◽  
Infinite Dimensional ◽  
Brst Operator ◽  
Finite Dimensional ◽  
Algebra Of Functions

In the study of the Type II superstring, it is useful to consider the BRST complex associated to the sum of two pure spinors. The cohomology of this complex is an infinite-dimensional vector space. It is also a finite-dimensional algebra over the algebra of functions of a single pure spinor. In this paper we study the multiplicative structure.

scholarly journals Cyclotomic Nazarov-Wenzl Algebras

2006 ◽  
Vol 182 ◽  
pp. 47-134 ◽  
Author(s):  
Susumu Ariki ◽  
Andrew Mathas ◽  
Hebing Rui
Keyword(s):  
Irreducible Representations ◽  
Arbitrary Field ◽  
Dimensional Algebra ◽  
Simple Modules ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Irreducible Modules ◽  
Brauer Algebras

AbstractNazarov [Naz96] introduced an infinite dimensional algebra, which he called the affine Wenzl algebra, in his study of the Brauer algebras. In this paper we study certain “cyclotomic quotients” of these algebras. We construct the irreducible representations of these algebras in the generic case and use this to show that these algebras are free of rank rn(2n−1)!! (when Ω is u-admissible). We next show that these algebras are cellular and give a labelling for the simple modules of the cyclotomic Nazarov-Wenzl algebras over an arbitrary field. In particular, this gives a construction of all of the finite dimensional irreducible modules of the affine Wenzl algebra.

scholarly journals Finite Dimensional Grading of the Virasoro Algebra

2007 ◽  
Vol 14 (3) ◽  
pp. 419-434
Author(s):  
Rubén A. Hidalgo ◽  
Irina Markina ◽  
Alexander Vasil'ev
Keyword(s):  
Univalent Functions ◽  
Virasoro Algebra ◽  
Energy Tensor ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Witt Algebra ◽  
Dimensional Algebra ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Universal Teichmüller Space

Abstract The Virasoro algebra is a central extension of the Witt algebra, the complexified Lie algebra of the sense preserving diffeomorphism group of the circle Diff 𝑆1. It appears in Quantum Field Theories as an infinite dimensional algebra generated by the coefficients of the Laurent expansion of the analytic component of the momentum-energy tensor, Virasoro generators. The background for the construction of the theory of unitary representations of Diff 𝑆1 is found in the study of Kirillov's manifold Diff 𝑆1=𝑆1. It possesses a natural Kählerian embedding into the universal Teichmüller space with the projection into the moduli space realized as an infinite-dimensional body of the coefficients of univalent quasiconformally extendable functions. The differential of this embedding leads to an analytic representation of the Virasoro algebra based on Kirillov's operators. In this paper we overview several interesting connections between the Virasoro algebra, Teichmüller theory, Löwner representation of univalent functions, and propose a finite-dimensional grading of the Virasoro algebra such that the grades form a hierarchy of finite dimensional algebras which, in their turn, are the first integrals of Liouville partially integrable systems for coefficients of univalent functions.

scholarly journals Interlacing methods and large indecomposables

1970 ◽  
Vol 3 (3) ◽  
pp. 337-348 ◽  
Author(s):  
S. E. Dickson ◽  
G. M. Kelly
Keyword(s):  
Artinian Ring ◽  
Finite Dimensional Algebra ◽  
Finitely Generated ◽  
Dimensional Algebra ◽  
Infinite Dimensional ◽  
Direct Sum ◽  
Number Of Generators ◽  
Finite Dimensional ◽  
Factor Module ◽  
Algebra Over A Field

The method of interlacing of modules, like amalgamation of groups, is a way of getting new objects from old. Briefly, the interlacing module we consider is a certain factor module of a direct sum of copies (finite or infinite) of an original module M. The conditions given in a previous paper by the first author in order that the interlacing module (using finitely many copies) be indecomposable are here greatly weakened, and we further allow the number of copies of the original to be infinite. R. Colby has shown that if R is a left artinian ring, the existence of a bound on the number of generators required for any indecomposable finitely-generated left R-module implies that R has a distributive lattice of two-sided ideals. This result is extended to rings whose identity is a sum of orthogonal local idempotents.For these rings the same distributivity is proved in case every indecomposable interlacing module of the above type which begins with an indecomposable projective M is finitely-generated. A consequence is that any finite-dimensional algebra over a field having infinitely many two-sided ideals has infinite-dimensional indecomposables.

scholarly journals Entire Analytic Functions of Unbounded Type on Banach Spaces and Their Lineability

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 150
Author(s):  
Andriy Zagorodnyuk ◽  
Anna Hihliuk
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Analytic Functions ◽  
Entire Functions ◽  
Dimensional Algebra ◽  
Dimensional Banach Space ◽  
Infinite Dimensional ◽  
Linear Subspaces ◽  
Infinite Dimensional Banach Space

In the paper we establish some conditions under which a given sequence of polynomials on a Banach space X supports entire functions of unbounded type, and construct some counter examples. We show that if X is an infinite dimensional Banach space, then the set of entire functions of unbounded type can be represented as a union of infinite dimensional linear subspaces (without the origin). Moreover, we show that for some cases, the set of entire functions of unbounded type generated by a given sequence of polynomials contains an infinite dimensional algebra (without the origin). Some applications for symmetric analytic functions on Banach spaces are obtained.

scholarly journals An FDA-Based Approach for Clustering Elicited Expert Knowledge

Stats ◽  
2021 ◽  
Vol 4 (1) ◽  
pp. 184-204
Author(s):  
Carlos Barrera-Causil ◽  
Juan Carlos Correa ◽  
Andrew Zamecnik ◽  
Francisco Torres-Avilés ◽  
Fernando Marmolejo-Ramos
Keyword(s):  
Functional Data ◽  
Expert Knowledge ◽  
Probability Distributions ◽  
Knowledge Elicitation ◽  
Parallel Analysis ◽  
Data Sets ◽  
Dimensional Problem ◽  
Prior Distributions ◽  
Infinite Dimensional ◽  
Finite Dimensional

Expert knowledge elicitation (EKE) aims at obtaining individual representations of experts’ beliefs and render them in the form of probability distributions or functions. In many cases the elicited distributions differ and the challenge in Bayesian inference is then to find ways to reconcile discrepant elicited prior distributions. This paper proposes the parallel analysis of clusters of prior distributions through a hierarchical method for clustering distributions and that can be readily extended to functional data. The proposed method consists of (i) transforming the infinite-dimensional problem into a finite-dimensional one, (ii) using the Hellinger distance to compute the distances between curves and thus (iii) obtaining a hierarchical clustering structure. In a simulation study the proposed method was compared to k-means and agglomerative nesting algorithms and the results showed that the proposed method outperformed those algorithms. Finally, the proposed method is illustrated through an EKE experiment and other functional data sets.

scholarly journals The Farkas lemma of Shimizu, Aiyoshi and Katayama

1985 ◽  
Vol 31 (3) ◽  
pp. 445-450 ◽  
Author(s):  
Charles Swartz
Keyword(s):  
Convex Programming ◽  
Infinite Dimensional ◽  
Farkas Lemma ◽  
Finite Dimensional

Shimizu, Aiyoshi and Katayama have recently given a finite dimensional generalization of the classical Farkas Lemma. In this note we show that a result of Pshenichnyi on convex programming can be used to give a generalization of the result of Shimizu, Aiyoshi and Katayama to infinite dimensional spaces. A generalized Farkas Lemma of Glover is also obtained.

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