Timeline for A generalized K- theory via generalized idempotents
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Mar 30, 2016 at 7:01 | comment | added | hänsel | @Simon: yes, I know. Soon I realized that the answer ist just that an $n+1$-idempotent element has spectrum contained in $\,{0,1/n,2/n,...,1\}$. Then everthing is immediately clear and easy. | |
| Mar 23, 2016 at 14:32 | comment | added | Simon Henry | @hänsel : That is not true : for each $n$, there is exactly $n$ famillies of $n$ mutually orthogonal projections in $\mathbb{C}$ (a one and $(n-1)$ zeros in the various possible order). As there is exactly $n$ elements in $E_n(\mathbb{C})$ I don't see the problem. | |
| Mar 21, 2016 at 7:34 | comment | added | Ali Taghavi | @hänsel thank you very much for your very helpfull comment. When I have accepted this answer, I did not pay attention to the point which you mentioned. | |
| Mar 20, 2016 at 18:55 | comment | added | hänsel | Somewhat strange as for example $A = \mathbf{C}$ even does not have mutually orthogonal Elements. | |
| Mar 27, 2014 at 3:41 | vote | accept | Ali Taghavi | ||
| Mar 22, 2016 at 21:59 | |||||
| Feb 1, 2014 at 19:15 | comment | added | Neil Strickland | You don't need any fancy functional calculus. The inverse is just $f^{-1}(a)=(p_1(a),\dotsc,p_n(a))$, where $p_i(t)\in\mathbb{C}[t]$ is the unique polynomial of degree $n$ such that $p_i(u_j)=\delta_{ij}$. | |
| Feb 1, 2014 at 18:26 | comment | added | Ali Taghavi | Some question on your answer:1)Is your statement true for a complex algebra( without any topological consideration, so without holomorphic functional calculus)? 2)what can we say if we are interested in pure algebraic generalized K theory(for rings) 3)According to your answer, do you belive that the three realations on generalized idempotents in banach algebras(Mouray Von.similarity, homotopy...) is well defined? Does it leads to triviality? $)could you please write the argument in your answer for banach algebras , explicitly? Thanks | |
| Feb 1, 2014 at 17:04 | history | answered | Neil Strickland | CC BY-SA 3.0 |