scholarly journals On the Schwinger Boson Representation of an Extended (M+1)(N+1)-Dimensional Algebra Containing the su(M+1)- and the su(N, 1)-Algebra

2000 ◽  
Vol 103 (2) ◽  
pp. 285-303
Author(s):  
A. Kuriyama ◽  
J. d. Providencia ◽  
M. Yamamura
Keyword(s):  
Dimensional Algebra ◽  
Boson Representation

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 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 Duality and socle generators for residual intersections

2019 ◽  
Vol 2019 (756) ◽  
pp. 183-226 ◽  
Author(s):  
David Eisenbud ◽  
Bernd Ulrich
Keyword(s):  
Gorenstein Ring ◽  
Jacobian Determinant ◽  
Finite Dimensional Algebra ◽  
Dimensional Algebra ◽  
Duality Results ◽  
Finite Dimensional ◽  
Algebra Over A Field ◽  
Residue Theory

AbstractWe prove duality results for residual intersections that unify and complete results of van Straten, Huneke–Ulrich and Ulrich, and settle conjectures of van Straten and Warmt.Suppose that I is an ideal of codimension g in a Gorenstein ring, and {J\subset I} is an ideal with {s=g+t} generators such that {K:=J:I} has codimension s. Let {{\overline{I}}} be the image of I in {{\overline{R}}:=R/K}.In the first part of the paper we prove, among other things, that under suitable hypotheses on I, the truncated Rees ring {{\overline{R}}\oplus{\overline{I}}\oplus\cdots\oplus{\overline{I}}{}^{t+1}} is a Gorenstein ring, and that the modules {{\overline{I}}{}^{u}} and {{\overline{I}}{}^{t+1-u}} are dual to one another via the multiplication pairing into {{{\overline{I}}{}^{t+1}}\cong{\omega_{\overline{R}}}}.In the second part of the paper we study the analogue of residue theory, and prove that, when {R/K} is a finite-dimensional algebra over a field of characteristic 0 and certain other hypotheses are satisfied, the socle of {I^{t+1}/JI^{t}\cong{\omega_{R/K}}} is generated by a Jacobian determinant.

Necessary conditions for power commuting in finite-dimensional algebras over a field

2018 ◽  
Vol 28 (5) ◽  
pp. 339-344
Author(s):  
Andrey V. Zyazin ◽  
Sergey Yu. Katyshev
Keyword(s):  
Necessary Conditions ◽  
Finite Dimensional Algebra ◽  
Dimensional Algebra ◽  
Finite Dimensional ◽  
Algebra Over A Field ◽  
Finite Dimensional Algebras

Abstract Necessary conditions for power commuting in a finite-dimensional algebra over a field are presented.

scholarly journals DISCUSSION ON THE SOLUTIONS IN DYSON BOSON REPRESENTATION

1989 ◽  
Vol 38 (10) ◽  
pp. 1673
Author(s):  
REN ZHONG-ZHOU ◽  
XU GONG-OU
Keyword(s):  
Boson Representation

Simple Type III Self-Injective Rings and Rings of Column-Finite Matrices

1987 ◽  
Vol 39 (4) ◽  
pp. 848-879
Author(s):  
K. C. O'Meara
Keyword(s):  
Simple Type ◽  
Common Occurrence ◽  
Dimensional Algebra ◽  
Type Iii ◽  
Division Rings ◽  
Information Transfers ◽  
Ore Domain

Relatively little is known about simple, Type III, right self-injective rings Q. This is despite their common occurrence, for example as Qmax(R) for any prime, nonsingular, countable-dimensional algebra R without uniform right ideals. (In particular Q can be constructed with a given field as its centre.) As with their directly finite, SP(1), right self-injective counterparts, division rings, there are few obvious invariants apart from the centre.One reason perhaps why little interest has been shown in their structure is that the usual construction of such Q, namely as a suitable Qmax(R), is not concrete enough; in general R sits far too loosely inside Q and not enough information transfers to Q from R. Thus, for example, taking R to be a non-right-Ore domain and Q = Qmax(R) tells us little about Q (although it has been conjectured that all Q arise this way).

scholarly journals Residually finite dimensional algebras and polynomial almost identities

2020 ◽  
pp. 2250038
Author(s):  
Michael Larsen ◽  
Aner Shalev
Keyword(s):  
Lie Algebra ◽  
Finite Index ◽  
Open Group ◽  
Finite Codimension ◽  
Finite Dimensional Algebra ◽  
Nilpotent Ideal ◽  
Dimensional Algebra ◽  
Residually Finite ◽  
Finite Dimensional ◽  
Theoretic Problem

Let [Formula: see text] be a residually finite dimensional algebra (not necessarily associative) over a field [Formula: see text]. Suppose first that [Formula: see text] is algebraically closed. We show that if [Formula: see text] satisfies a homogeneous almost identity [Formula: see text], then [Formula: see text] has an ideal of finite codimension satisfying the identity [Formula: see text]. Using well known results of Zelmanov, we conclude that, if a residually finite dimensional Lie algebra [Formula: see text] over [Formula: see text] is almost [Formula: see text]-Engel, then [Formula: see text] has a nilpotent (respectively, locally nilpotent) ideal of finite codimension if char [Formula: see text] (respectively, char [Formula: see text]). Next, suppose that [Formula: see text] is finite (so [Formula: see text] is residually finite). We prove that, if [Formula: see text] satisfies a homogeneous probabilistic identity [Formula: see text], then [Formula: see text] is a coset identity of [Formula: see text]. Moreover, if [Formula: see text] is multilinear, then [Formula: see text] is an identity of some finite index ideal of [Formula: see text]. Along the way we show that if [Formula: see text] has degree [Formula: see text], and [Formula: see text] is a finite [Formula: see text]-algebra such that the probability that [Formula: see text] (where [Formula: see text] are randomly chosen) is at least [Formula: see text], then [Formula: see text] is an identity of [Formula: see text]. This solves a ring-theoretic analogue of a (still open) group-theoretic problem posed by Dixon,

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.

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