scholarly journals OFF-CRITICAL CURRENT ALGEBRAS

1995 ◽  
Vol 10 (12) ◽  
pp. 1717-1736 ◽  
Author(s):  
E. ABDALLA ◽  
M.C.B. ABDALLA ◽  
G. SOTKOV ◽  
M. STANISHKOV
Keyword(s):  
Abelian Group ◽  
Critical Current ◽  
General Structure ◽  
Dimensional Algebra ◽  
Fermionic Model ◽  
Infinite Dimensional ◽  
Conformally Invariant ◽  
Current Algebras

We discuss the infinite-dimensional algebras appearing in integrable perturbations of conformally invariant theories, with special emphasis on the structure of the consequent non-Abelian infinite-dimensional algebra generalizing W∞ to the case of a non-Abelian group. We prove that the pure left sector as well as the pure right sector of the thus-obtained algebra coincides with the conformally invariant case. The mixed sector is more involved, although the general structure seems to be near to being unraveled. We also find some subalgebras that correspond to Kac-Moody algebras. The constraints imposed by the algebras are very strong and, in the case of the massive deformation of a non-Abelian fermionic model, the symmetry alone is enough to fix the two- and three-point functions of the theory.

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 On Primitive Ideals in Graded Rings

2008 ◽  
Vol 51 (3) ◽  
pp. 460-466 ◽  
Author(s):  
Agata Smoktunowicz
Keyword(s):  
Prime Ideal ◽  
Jacobson Radical ◽  
Graded Rings ◽  
Dimensional Algebra ◽  
Infinite Dimensional ◽  
Primitive Ideals ◽  
Nil Ring

AbstractLet R = be a graded nil ring. It is shown that primitive ideals in R are homogeneous. Let A = be a graded non-PI just-infinite dimensional algebra and let I be a prime ideal in A. It is shown that either I = ﹛0﹜ or I = A. Moreover, A is either primitive or Jacobson radical.

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 GROUP GRADINGS ON FINITARY SIMPLE LIE ALGEBRAS

2012 ◽  
Vol 22 (05) ◽  
pp. 1250046 ◽  
Author(s):  
YURI BAHTURIN ◽  
MATEJ BREŠAR ◽  
MIKHAIL KOCHETOV
Keyword(s):  
Abelian Group ◽  
Lie Algebras ◽  
Vector Spaces ◽  
Closed Field ◽  
Dimensional Vector ◽  
Linear Transformations ◽  
Special Linear ◽  
Infinite Dimensional ◽  
Group Gradings ◽  
Arbitrary Abelian Group

We classify, up to isomorphism, all gradings by an arbitrary abelian group on simple finitary Lie algebras of linear transformations (special linear, orthogonal and symplectic) on infinite-dimensional vector spaces over an algebraically closed field of characteristic different from 2.

scholarly journals LARGE N MATRIX MECHANICS ON THE LIGHT-CONE

2002 ◽  
Vol 17 (11) ◽  
pp. 1517-1542 ◽  
Author(s):  
M. B. HALPERN ◽  
CHARLES B. THORN
Keyword(s):  
Light Cone ◽  
Eigenvalue Problems ◽  
Hamiltonian Formulation ◽  
Cuntz Algebra ◽  
Conserved Quantities ◽  
Basic Tool ◽  
Dimensional Algebra ◽  
Infinite Dimensional ◽  
Matrix Mechanics ◽  
Large N

We report a simplification in the large N matrix mechanics of light-cone matrix field theories. The absence of pure creation or pure annihilation terms in the Hamiltonian formulation of these theories allows us to find their reduced large N Hamiltonians as explicit functions of the generators of the Cuntz algebra. This opens up a free-algebraic playground of new reduced models — all of which exhibit new hidden conserved quantities at large N and all of whose eigenvalue problems are surprisingly simple. The basic tool we develop for the study of these models is the infinite dimensional algebra of all normal-ordered products of Cuntz operators, and this algebra also leads us to a special number-conserving subset of these models, each of which exhibits an infinite number of new hidden conserved quantities at large N.

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.

THE GENERAL STRUCTURE OF G-GRADED CONTRACTIONS OF LIE ALGEBRAS, II: THE CONTRACTED LIE ALGEBRA

2006 ◽  
Vol 18 (06) ◽  
pp. 655-711 ◽  
Author(s):  
EVELYN WEIMAR-WOODS
Keyword(s):  
Abelian Group ◽  
Detailed Analysis ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Finite Abelian Group ◽  
General Structure ◽  
Complete Characterization ◽  
Proper Subset

We continue our study of G-graded contractions γ of Lie algebras where G is an arbitrary finite Abelian group. We compare them with contractions, especially with respect to their usefulness in physics. (Note that the unfortunate terminology "graded contraction" is confusing since they are, by definition, not contractions.)We give a complete characterization of continuous G-graded contractions and note that they are equivalent to a proper subset of contractions. We study how the structure of the contracted Lie algebra Lγdepends on γ, and show that, for discrete graded contractions, applications in physics seem unlikely.Finally, with respect to applications to representations and invariants of Lie algebras, a comparison of graded contractions with contractions reveals the insurmountable defects of the graded contraction approach. In summary, our detailed analysis shows that graded contractions are clearly not useful in physics.

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