Infinite-dimensional algebra of general covariance group as the closure of finite-dimensional algebras of conformal and linear groups

2008 ◽  
pp. 397-399
Author(s):  
V. I. Ogievetsky
Keyword(s):  
Linear Groups ◽  
General Covariance ◽  
Dimensional Algebra ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Covariance Group ◽  
Finite Dimensional Algebras

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 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 Involutions on finite-dimensional algebras over real closed fields

2004 ◽  
Vol 77 (1) ◽  
pp. 123-128 ◽  
Author(s):  
W. D. Munn
Keyword(s):  
Characteristic Zero ◽  
Real Closed Field ◽  
Closed Field ◽  
Finite Dimensional Algebra ◽  
Dimensional Algebra ◽  
Algebraically Closed Field ◽  
Real Closed Fields ◽  
Finite Dimensional ◽  
Closed Fields ◽  
Finite Dimensional Algebras

AbstractIt is shown that the following conditions on a finite-dimensional algebra A over a real closed field or an algebraically closed field of characteristic zero are equivalent: (i) A admits a special involution, in the sense of Easdown and Munn, (ii) A admits a proper involution, (iii) A is semisimple.

scholarly journals Simple reflexive modules over finite-dimensional algebras

2020 ◽  
pp. 2150166
Author(s):  
Claus Michael Ringel
Keyword(s):  
Finite Dimensional Algebra ◽  
Dimensional Algebra ◽  
Large Classes ◽  
Indecomposable Modules ◽  
Simple Modules ◽  
Finite Dimensional ◽  
Reflexive Modules ◽  
Finite Dimensional Algebras

Let [Formula: see text] be a finite-dimensional algebra. If [Formula: see text] is self-injective, then all modules are reflexive. Marczinzik recently has asked whether [Formula: see text] has to be self-injective in case all the simple modules are reflexive. Here, we exhibit an 8-dimensional algebra which is not self-injective, but such that all simple modules are reflexive (actually, for this example, the simple modules are the only non-projective indecomposable modules which are reflexive). In addition, we present some properties of simple reflexive modules in general. Marczinzik had motivated his question by providing large classes [Formula: see text] of algebras such that any algebra in [Formula: see text] which is not self-injective has simple modules which are not reflexive. However, as it turns out, most of these classes have the property that any algebra in [Formula: see text] which is not self-injective has simple modules which are not even torsionless.

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 Irreducible locally nilpotent finitary skew linear groups

1995 ◽  
Vol 38 (1) ◽  
pp. 63-76 ◽  
Author(s):  
B. A. F. Wehrfritz
Keyword(s):  
Linear Group ◽  
Division Ring ◽  
Linear Groups ◽  
Locally Finite ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Finitary Linear Group ◽  
Locally Nilpotent ◽  
Finitary Linear ◽  
Finite Dimensional Case

Let V be a left vector space over the arbitrary division ring D and G a locally nilpotent group of finitary automorphisms of V (automorphisms g of V such that dimDV(g-1)<∞) such that V is irreducible as D-G bimodule. If V is infinite dimensional we show that such groups are very rare, much rarer than in the finite-dimensional case. For example we show that if dimDV is infinite then dimDV = |G| = ℵ0 and G is a locally finite q-group for some prime q ≠ char D. Moreover G is isomorphic to a finitary linear group over a field. Examples show that infinite-dimensional such groups G do exist. Note also that there exist examples of finite-dimensional such groups G that are not isomorphic to any finitary linear group over a field. Generally the finite-dimensional examples are more varied.

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.

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