Volume 33 • Number 3 • 2010   • Entropy for a Pair of Subalgebras via Automorphisms Marie Choda Abstract. This is an expository survey article based on a talk for the Special Session (Operator Algebra) in AMC 2009. For two subalgebras A and B of a finite von Neumann algebra M, we discuss a modified version h(A|B) of the Connes-Strømer relative entropy H(A|B). As one of the most elementary examples, we pick two maximal abelian *-subalgebras A, B of the n × n complex matrices Mn(ℂ), and show relations between h(A|B) and the entropy for unistochastic matrices. Also we show related results in the case of a pair of subfactors of a type II1 factor. 2010 Mathematics Subject Classification: 46L55, 46L37, 46L40. Full text: PDF