Boolean algebras and the Calkin algebra

Speaker(s)

Piotr Koszmider

Affiliation

IM PAN

Language of the talk

Polish

Date

Nov. 19, 2025, 4:15 p.m.

Room

room 4050

Seminar

Topology and Set Theory Seminar

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The Calkin C*-algebra Q can be considered as the non-abelian analogue of the Boolean algebra P(N)/Fin.
It is defined as the quotient B/K of the algebra B of all linear bounded  operators on a separable Hilbert space H divided by the ideal K of compact operators on H. It contains many copies of the algebra P(N)/Fin. "Masa" stands for maximal abelian (self-adjoint) subalgebra. Many copies of P(N)/Fin generate masas of Q. We will discuss old and new, ZFC and consistency results concerning diverse masas of Q generated by Boolean algebras (i.e., of the form C(K) where K is totally disconnected Hausdorff space). 
Details of the new constructions will be presented at IMPAN seminars  on 20.11 and 27.11:
https://piotrkoszmider.github.io/seminar/

 

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