Representation theory and numerical AF-invariants : the representations and centralizers of certain states on Od
著者
書誌事項
Representation theory and numerical AF-invariants : the representations and centralizers of certain states on Od
（Memoirs of the American Mathematical Society, no. 797）
American Mathematical Society, 2004
大学図書館所蔵 全16件
注記
"March 2004, volume 168, number 797 (second of 4 numbers)."
Includes bibliographical references (p. 166-169)
内容説明・目次
内容説明
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 $S_{\alpha_{<!-- -->{}}}^{<!-- -->{}}S_{\alpha_{<!-- -->{}}}^{\ast}=S_{\alpha_{1}}^{<!-- -->{}}\cdot s S_{\alpha_{k}}^{<!-- -->{}}S_{\alpha_{k}}^{\ast}\cdots S_{\alpha_{1}}^{\ast}$ 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 of this title are devoted to finding effective methods to decide isomorphism and non-isomorphism in this class of AF-algebras.
目次
Part A. Representation theory Part B. Numerical AF-invariants Bibliography List of figures List of tables List of terms and symbols.
「Nielsen BookData」 より