Reflexive Representations of Algebras

1995 ◽  
pp. 193-208
Author(s):  
K. R. Fuller
Keyword(s):  
Representations Of Algebras

Positive Forms on Nuclear *-Algebras and Their Integral Representations

1990 ◽  
Vol 42 (3) ◽  
pp. 410-469 ◽  
Author(s):  
Alain Bélanger ◽  
Erik G. F. Thomas
Keyword(s):  
Integral Representation ◽  
Positive Cone ◽  
Approximate Identity ◽  
Integral Representations ◽  
Regularity Conditions ◽  
Direct Integral ◽  
Positive Form ◽  
Representations Of Algebras ◽  
Almost All ◽  
Order Intervals

Abstract.The main result of this paper establishes the existence and uniqueness of integral representations of KMS functionals on nuclear *- algebras. Our first result is about representations of *-algebras by means of operators having a common dense domain in a Hilbert space. We show, under certain regularity conditions, that (Powers) self-adjoint representations of a nuclear *-algebra, which admit a direct integral decomposition, disintegrate into representations which are almost all self-adjoint. We then define and study the class of self-derivative algebras. All algebras with an identity are in this class and many other examples are given. We show that if is a self-derivative algebra with an equicontinuous approximate identity, the cone of all positive forms on is isomorphic to the cone of all positive invariant kernels on These in turn correspond bijectively to the invariant Hilbert subspaces of the dual space This shows that if is a nuclear -space, the positive cone of has bounded order intervals, which implies that each positive form on has an integral representation in terms of the extreme generators of the cone. Given a continuous exponentially bounded one-parameter group of *-automorphisms of we can define the subcone of all invariant positive forms satisfying the KMS condition. Central functionals can be viewed as KMS functionals with respect to a trivial group action. Assuming that is a self-derivative algebra with an equicontinuous approximate identity, we show that the face generated by a self-adjoint KMS functional is a lattice. If is moreover a nuclear *-algebra the previous results together imply that each self-adjoint KMS functional has a unique integral representation by means of extreme KMS functionals almost all of which are self-adjoint.

scholarly journals Maximal subalgebras of finite-dimensional algebras

2019 ◽  
Vol 31 (5) ◽  
pp. 1283-1304 ◽  
Author(s):  
Miodrag Cristian Iovanov ◽  
Alexander Harris Sistko
Keyword(s):  
Associative Algebra ◽  
Complete Classification ◽  
Maximal Subalgebras ◽  
Incidence Algebras ◽  
Finite Dimensional ◽  
Semisimple Algebras ◽  
Closed Fields ◽  
Representations Of Algebras ◽  
Algebraically Closed Fields ◽  
Full Classification

AbstractWe study maximal associative subalgebras of an arbitrary finite-dimensional associative algebra B over a field {\mathbb{K}} and obtain full classification/description results of such algebras. This is done by first obtaining a complete classification in the semisimple case and then lifting to non-semisimple algebras. The results are sharpest in the case of algebraically closed fields and take special forms for algebras presented by quivers with relations. We also relate representation theoretic properties of the algebra and its maximal and other subalgebras and provide a series of embeddings between quivers, incidence algebras and other structures which relate indecomposable representations of algebras and some subalgebras via induction/restriction functors. Some results in literature are also re-derived as a particular case, and other applications are given.

scholarly journals On Representations of *-Algebras in Mathematical Physics

1996 ◽  
Vol 3 (1-2) ◽  
pp. 160-163
Author(s):  
Vasyl’ L. Ostrovs’KYĭ ◽  
Yuriĭ S. Samoĭlenko
Keyword(s):  
Mathematical Physics ◽  
Representations Of Algebras
Sign in / Sign up

Export Citation Format

Share Document