Search results for "Subalgebra"

Extended-order algebras as a generalization of posets

2011

Motivated by the recent study of several researchers on extended-order algebras, introduced by C. Guido and P. Toto as a possible common framework for the majority of algebraic structures used in many-valued mathematics, the paper focuses on the properties of homomorphisms of the new structures, considering extended-order algebras as a generalization of partially ordered sets. The manuscript also introduces the notion of extended-relation algebra providing a new framework for developing the theory of rough sets.

Banach Partial *-Algebras and Quantum Models

2007

C*-algebras are, as known, the basic mathematical ingredient of the Haag- Kastler (Haag and Kastler 1964) algebraic approach to quantum systems, with infinitely many degrees of freedom. The usual procedure starts, in fact, with associating to each bounded region V of the configuration space of the system the C*-algebra AV of local observables in V. The uniform completion A of the algebra generated by the AV ’s is then considered as the C*-algebra of observables of the system

Quantum deformations of singletons and of free zero-mass fields

1993

We consider quantum deformations of the real symplectic (or anti-De Sitter) algebra sp(4), ℝ ≅ spin(3, 2) and of its singleton and (4-dimensional) zero-mass representations. For q a root of −1, these representations admit finite-dimensional unitary subrepresentations. It is pointed out that Uq(sp(4, ℝ)), unlike Uq(su(2, 2)), contains Uq(sl2) as a quantum subalgebra.

MR2905225 Rowe, Stephen; Fang, Junsheng; Larson, David R. P1 subalgebras of Mn(C). Involve 4 (2011), no. 3, 213–250. (Reviewer: Camillo Trapani)

2012

An Operator Theoretical Approach to Enveloping ϕ* - and C* - Algebras of Melrose Algebras of Totally Characteristic Pseudodifferential Operators

1998

Let X be a compact manifold with boundary. It will be shown (Theorem 3.4) that the small Melrose algebra A≔ ϕb,cl (χ,bΩ1/2) (cf. [22], [23]) of classical, totally characteristic pseudodifferential operators carries no topology such that it is a topological algebra with an open group of invertible elements, in particular, the algebra A cannot be spectrally invariant in any C* – algebra. On the other hand, the symbolic structure of A can be extended continuously to the C* – algebra B generated by A as a subalgebra of ζ(σbL2(χ, bΩ1/2)) by a generalization of a method of Gohberg and Krupnik. Furthermore, A is densely embedded in a Frechet algebra A ⊆ B which is a ϕ* – algebra in the sense of Gr…

THE GROUP OF AUTOMORPHISMS OF THE SEMIGROUP OF ENDOMORPHISMS OF FREE COMMUTATIVE AND FREE ASSOCIATIVE ALGEBRAS

2007

Let W(X) be a free commutative or a free associative algebra. The group of automorphisms of the semigroup End (W(X)) is studied.

Annihilators of tensor density modules

2007

Abstract We describe the two-sided ideals in the universal enveloping algebras of the Lie algebras of vector fields on the line and the circle which annihilate the tensor density modules. Both of these Lie algebras contain the projective subalgebra, a copy of sl 2 . The restrictions of the tensor density modules to this subalgebra are duals of Verma modules (of sl 2 ) for Vec ( R ) and principal series modules (of sl 2 ) for Vec ( S 1 ) . Thus our results are related to the well-known theorem of Duflo describing the annihilating ideals of Verma modules of reductive Lie algebras. We find that, in general, the annihilator of a tensor density module of Vec ( R ) or Vec ( S 1 ) is generated by …

Quasi *-algebras and generalized inductive limits of C*-algebras

2011