Author: Ola BratteliPublisher:
ISBN:
Category :
Languages : en
Pages : 178
Book Description
Representation theory and numerical AF-invariants
Author: Ola BratteliRepresentation Theory and Numerical AF-Invariants
Author: Ola BratteliPublisher: American Mathematical Society(RI)
ISBN: 9781470403959
Category : Ergodic theory
Languages : en
Pages : 202
Book Description
Representation Theory and Numerical AF-Invariants
Author: Ola BratteliPublisher: American Mathematical Soc.
ISBN: 0821834916
Category : Mathematics
Languages : en
Pages : 202
Book Description
Part A. Representation theory Part B. Numerical AF-invariants Bibliography List of figures List of tables List of terms and symbols.
Representation Theory and Numerical AF-Invariants
Author: Ola Bratteli Palle E. T. J¿rgensen Vasyl OstrovskyiPublisher: American Mathematical Soc.
ISBN: 9780821865194
Category : Ergodic theory
Languages : en
Pages : 206
Book Description
Let $\mathcal{O}_{d}$ be the Cuntz algebra on generators $S_{1},\dots,S_{d}$, $2\leq d<\infty$. Let $\mathcal{D}_{d}\subset\mathcal{O}_{d}$ be the abelian subalgebra generated by monomials $S_{\alpha_{{}}}^{{}}S_{\alpha_{{}} }^{\ast}=S_{\alpha_{1}}^{{}}\cdots S_{\alpha_{k}}^{{}}S_{\alpha_{k}}^{\ast }\cdots S_{\alpha_{1}}^{\ast}$ where $\alpha=\left(\alpha_{1}\dots\alpha _{k}\right)$ ranges over all multi-indices formed from $\left\{ 1,\dots,d\right\}$. In any representation of $\mathcal{O}_{d}$, $\mathcal{D}_{d}$ may be simultaneously diagonalized. Using $S_{i}^{{}}\left( S_{\alpha}^{{}}S_{\alpha}^{\ast}\right) =\left( S_{i\alpha}^{{}}S_{i\alpha }^{\ast}\right) S_{i}^{{}}$, we show that the operators $S_{i}$ from a general representation of $\mathcal{O}_{d}$ may be expressed directly in terms of the spectral representation of $\mathcal{D}_{d}$. We use this in describing a class of type $\mathrm{III}$ representations of $\mathcal{O}_{d}$ and corresponding endomorphisms, and the heart of the memoir is a description of an associated family of AF-algebras arising as the fixed-point algebras of the associated modular automorphism groups. Chapters 5-18 are devoted to finding effective methods to decide isomorphism and non-isomorphism in this class of AF-algebras.
Operators and Representation Theory
Author: Palle E.T. JorgensenPublisher: Courier Dover Publications
ISBN: 0486815722
Category : Science
Languages : en
Pages : 307
Book Description
Three-part treatment covers background material on definitions, terminology, operators in Hilbert space domains of representations, operators in the enveloping algebra, spectral theory; and covariant representation and connections. 2017 edition.
Classification and Probabilistic Representation of the Positive Solutions of a Semilinear Elliptic Equation
Author: Benoît MselatiPublisher: American Mathematical Soc.
ISBN: 0821835092
Category : Mathematics
Languages : en
Pages : 146
Book Description
Concerned with the nonnegative solutions of $\Delta u = u^2$ in a bounded and smooth domain in $\mathbb{R}^d$, this title intends to prove that they are uniquely determined by their fine trace on the boundary as defined in [DK98a], answering a major open question of [Dy02].
Equivariant, Almost-Arborescent Representations of Open Simply-Connected 3-Manifolds; A Finiteness Result
Author: Valentin PoenaruPublisher: American Mathematical Soc.
ISBN: 0821834606
Category : Mathematics
Languages : en
Pages : 104
Book Description
Shows that at the cost of replacing $V DEGREES3$ by $V_h DEGREES3 = \{V DEGREES3$ with very many holes $\}$, we can always find representations $X DEGREES2 \stackrel {f} {\rightarrow} V DEGREES3$ with $X DEGREES2$ locally finite and almost-arborescent, with $\Psi (f)=\Phi (f)$, and with the ope
Representation Type of Commutative Noetherian Rings III: Global Wildness and Tameness
Author: Lee KlinglerPublisher: American Mathematical Soc.
ISBN: 0821837389
Category : Mathematics
Languages : en
Pages : 187
Book Description
This memoir completes the series of papers beginning with [KL1,KL2], showing that, for a commutative noetherian ring $\Lambda$, either the category of $\Lambda$-modules of finite length has wild representation type or else we can describe the category of finitely generated $\Lambda$-modules, including their direct-sum relations and local-global relations. (There is a possible exception to our results, involving characteristic 2.)
The Complete Dimension Theory of Partially Ordered Systems with Equivalence and Orthogonality
Author: K. R. GoodearlPublisher: American Mathematical Soc.
ISBN: 0821837168
Category : Mathematics
Languages : en
Pages : 134
Book Description
Introduction Partial commutative monoids Continuous dimension scales Espaliers Classes of espaliers Bibliography Index
Ergodic Theory of Equivariant Diffeomorphisms: Markov Partitions and Stable Ergodicity
Author: Mike FieldPublisher: American Mathematical Soc.
ISBN: 0821835998
Category : Mathematics
Languages : en
Pages : 113
Book Description
On the assumption that the $\Gamma$-orbits all have dimension equal to that of $\Gamma$, this title shows that there is a naturally defined $F$- and $\Gamma$-invariant measure $\nu$ of maximal entropy on $\Lambda$ (it is not assumed that the action of $\Gamma$ is free).