User sion - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-19T04:46:03Z http://mathoverflow.net/feeds/user/13739 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/120338/general-recipe-for-building-c-algebras-out-of-combinatorial-object General recipe for building C*-algebras out of combinatorial object SiOn 2013-01-30T16:57:07Z 2013-02-04T06:29:31Z <p>I want to ask what should be a nice way to build C*-algebras out of objects like groups, inverse-semigroups, semigroups, ringgs or graphs. I know there are well known construction of C*-algebras out of those objects; but I want to understand what philosophy lies under the recipe. Say for discrete groups I know group C*-algebras are made of as universal object of unitary elements of groups elements with relations coming from group operation. Now what I understand is they take unitary because if we fix an element $g$ in the group $G$, the map $T_g:G\rightarrow G$ defined by $T_g(h)=gh$ is one-one onto morphism. For Ring C*-algebras also this works. In that case where the map is not onty they take isometry. But my confusion starts with graph C*-algebra. I don't understand why they take projections for vertices and partial isometrys for edges (and the given relations). </p> http://mathoverflow.net/questions/120128/realizing-universal-c-algebras-as-concrete-c-algebras Realizing universal C*-algebras as concrete C*-algebras SiOn 2013-01-28T17:01:03Z 2013-02-01T23:54:08Z <p>How do I in general realize a universal C*-algebra generated by some generators and relation as concrete C*-algebras? For example, I know that universal C*-algebra generated by a single unitary is $C(\mathbb{T})$ by functional calculas. I am looking at the following examples to work on:</p> <ol> <li>universal C*-algebra generated by single self-adjoint element whose norm is 1.</li> <li>universal C*-algebra generated by single positive element whose norm is 1.</li> <li>universal C*-algebra generated by single normal element whose norm is 1.</li> <li>universal C*-algebra generated by single projection.</li> </ol> http://mathoverflow.net/questions/58820/image-of-a-discontinuous-linear-functional Comment by SiOn SiOn 2011-03-18T09:21:05Z 2011-03-18T09:21:05Z kernel is not closed I guess... http://mathoverflow.net/questions/58820/image-of-a-discontinuous-linear-functional Comment by SiOn SiOn 2011-03-18T09:03:59Z 2011-03-18T09:03:59Z for finite dimensional spaces every linear map is continuous