1.Mathematics Department,University of California,Berkeley,USA;2.Department of Mathematics,Columbia University,New York,USA
Abstract:
In this series of papers we show that there are exactly ten subfactors, other than A∞ subfactors, of index between 4 and 5. Previously this classification was known up to index ({3+sqrt{3}}). In the first paper we give an analogue of Haagerup’s initial classification of subfactors of index less than ({3+sqrt{3}}), showing that any subfactor of index less than 5 must appear in one of a large list of families. These families will be considered separately in the three subsequent papers in this series.
