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Infinite Dimensional Central Simple Regular Algebras with Outer Derivations
Lobachevskii Journal of Mathematics ( IF 0.8 ) Pub Date : 2020-07-16 , DOI: 10.1134/s1995080220030063 Sh. Ayupov , K. Kudaybergenov
中文翻译:
具有外导数的无穷维中央简单正则代数
更新日期:2020-07-16
Lobachevskii Journal of Mathematics ( IF 0.8 ) Pub Date : 2020-07-16 , DOI: 10.1134/s1995080220030063 Sh. Ayupov , K. Kudaybergenov
Abstract
We give an example of infinite dimensional central simple (von Neumann) regular algebra with outer derivations. Given the algebra \(S(M)\) of all measurable operators affiliated with the type II\({}_{1}\) hyperfinite factor \(M\) we construct its \(\ast\)-subalgebra \(\mathcal{R}_{\infty}\) which is dense in the measure topology. We prove that this algebra has a derivation which is discontinuous in the measure topology and hence is non-inner. We show that the algebra \(\mathcal{R}_{\infty}\) admits also a continuous (in the measure topology) derivation, implemented by a measurable operator, but which is still an outer derivation.中文翻译:
具有外导数的无穷维中央简单正则代数