{"product_id":"9780821834916","title":"Representation Theory and Numerical AF-invariants","description":"\u003cp\u003eLet $\\mathcal{O}{d}$ be the Cuntz algebra on generators $S{1},\\dots,S{d}$, $2\\leq d{}}}^{{}}S{\\alpha{{}}}^{\\ast}=S{\\alpha{1}}^{{}}\\cdot s S{\\alpha{k}}^{{}}S{\\alpha{k}}^{\\ast}\\cdots S{\\alpha{1}}^{\\ast}$ 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.\u003c\/p\u003e","brand":"Exclusive Books Online","offers":[{"title":"Default Title","offer_id":52684773785918,"sku":"9780821834916","price":0.0,"currency_code":"ZAR","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4357\/7662\/files\/9780821834916.jpg?v=1764858473","url":"https:\/\/exclusivebooks.co.za\/products\/9780821834916","provider":"Exclusive Books Online","version":"1.0","type":"link"}