The Curvature Invariant of a Non-commuting N-tuple
نویسنده
چکیده
Non-commutative versions of Arveson’s curvature invariant and Euler characteristic for a commuting n-tuple of operators are introduced. The noncommutative curvature invariant is sensitive enough to determine if an ntuple is free. In general both invariants can be thought of as measuring the freeness or curvature of an n-tuple. The connection with dilation theory provides motivation and exhibits relationships between the invariants. A new class of examples is used to illustrate the differences encountered in the noncommutative setting and obtain information on the ranges of the invariants. The curvature invariant is also shown to be upper semi-continuous.
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