Inductive limits of finite dimensional hermitian symmetric spaces and Ktheory
Abstract
KTheory for hermitian symmetric spaces of noncompact type, as developed recently by the authors, allows to put Cartan's classification into a homological perspective. We apply this method to the case of inductive limits of finite dimensional hermitian symmetric spaces. This might be seen as an indication of how much more powerful the homological theory is in comparison to the more classical approach. When seen from high above, we follow the path laid out by a similar result in the theory of C*algebras. Important is a clear picture of the behavior of morphisms between bounded symmetric domains of finite dimensions, which is more complex than in the C*case, as well as an accessible Ktheory. We furthermore have to slightly modify the invariant from our previous work. Roughly, we use traces left by coroot lattices on Kgroups, instead of coroots themselves, which had been used previously.
 Publication:

arXiv eprints
 Pub Date:
 September 2016
 DOI:
 10.48550/arXiv.1609.06921
 arXiv:
 arXiv:1609.06921
 Bibcode:
 2016arXiv160906921B
 Keywords:

 Mathematics  KTheory and Homology;
 Mathematics  Operator Algebras;
 17C10;
 17C37;
 19E99;
 32M15;
 46G20;
 46L08;
 46L80;
 46M15;
 46M40;
 46T05;
 53B35;
 53C35;
 58B20;
 58B25