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Bert Lindenhovius

Publications and source records attributed to Bert Lindenhovius.

20 records · Page 2Linked to original sources
arXiv2016

Classifying finite-dimensional C*-algebras by posets of their commutative C*-subalgebras

We consider the functor C that to a unital C*-algebra A assigns the partial order set C(A) of its commutative C*-subalgebras ordered by inclusion. We investigate how some C*-algebraic properties translate under the action of C to order-theoretical properties. In particular, we show that A is finite dimensional if and only C(A) satisfies certain chain conditions. We eventually show that if A and B are C*-algebras such that A is finite dimensional and C(A) and C(B) are order isomorphic, then A and B must be *-isomorphic.

math.OA↗
arXiv2014

Grothendieck topologies on a poset

We investigate Grothendieck topologies (in the sense of sheaf theory) on a poset $¶$ that are generated by some subset of $¶$. We show that such Grothendieck topologies exhaust all possibilities if and only if $¶$ is Artinian. If $¶$ is not Artinian, other families of Grothendieck topologies on $¶$ exist that are not generated by some subset of $¶$, but even those are related to the Grothendieck topologies generated by subsets. Furthermore, we investigate several notions of equivalences of Grothendieck topologies, and using a posetal version of the Comparison Lemma, a sheaf-theoretic result known as the Comparison Lemma, going back to Grothendieck et al \cite{SGA4}, we calculate the sheaves with respect to most of the Grothendieck topologies we have found.

math.CT↗