高明杵教授（路易斯安那基督教大学）

时间：12月10日（本周五）上午9：00。

摘要:

Among Kadison’s famous problems on operator algebras (raised at the Baton Rouge conference in 1967), there is only one dealing with non-closed *-self-adjoint subalgebras of linear operators (No. 15): if every finitely generated *-subalgebra (of operators on a Hilbert space) such that each self-adjoint element there has a finite spectrum is a finite dimensional algebra. Recently, M. Mori connected the property that every self-adjoint has a finite spectrum in the algebra to von Neumann’s concept of regular rings, which von Neumann introduced in developing continuous geometry in 1936-37. Thus, Mori called such a *-subalgebra an R*-algebra (here R stands for von Neumann’s regular). A commutative R*-algebra is the set of all finite ranged complex-valued Boolean functions associated with a generalized Boolean algebra of subsets of a set. The forementioned Kadision’s question is equivalent to the question that whether every R*-algebra is approximately finite (like AF algebras in C*-algebras). In a philosophical perspective, C*-algebras are noncommutative topology, von Neumann algebras are noncommutative measure/probability theory, and R*-algebras would be noncommutative Boolean algebras. Thus, the study on R*-algebras would expend the realm of noncommutative mathematics, expecting further applications in quantum physics. In this talk, we introduce this newly raised research field and consider some open questions.

邀请人：侯绳照