5,991 research outputs found
Coincidence site modules in 3-space
The coincidence site lattice (CSL) problem and its generalization to
Z-modules in Euclidean 3-space is revisited, and various results and
conjectures are proved in a unified way, by using maximal orders in quaternion
algebras of class number 1 over real algebraic number fields.Comment: 25 page
Nonunital spectral triples and metric completeness in unbounded KK-theory
By considering the general properties of approximate units in differentiable
algebras, we are able to present a unified approach to characterising
completeness of spectral metric spaces, existence of connections on modules,
and the lifting of Kasparov products to the unbounded category. In particular,
by strengthening Kasparov's technical theorem, we show that given any two
composable KK-classes, we can find unbounded representatives whose product can
be constructed to yield an unbounded representative of the Kasparov product.Comment: 65 page
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