514 research outputs found
Constructing KMS states from infinite-dimensional spectral triples
We construct KMS-states from -summable semifinite spectral
triples and show that in several important examples the construction coincides
with well-known direct constructions of KMS-states for naturally defined flows.
Under further summability assumptions the constructed KMS-state can be computed
in terms of Dixmier traces. For closed manifolds, we recover the ordinary
Lebesgue integral. For Cuntz-Pimsner algebras with their gauge flow, the
construction produces KMS-states from traces on the coefficient algebra and
recovers the Laca-Neshveyev correspondence. For a discrete group acting on its
Stone-\v{C}ech boundary, we recover the Patterson-Sullivan measures on the
Stone-\v{C}ech boundary for a flow defined from the Radon-Nikodym cocycle.Comment: 66 page
Partial silting objects and smashing subcategories
We study smashing subcategories of a triangulated category with coproducts
via silting theory. Our main result states that for derived categories of dg
modules over a non-positive differential graded ring, every compactly generated
localising subcategory is generated by a partial silting object. In particular,
every such smashing subcategory admits a silting t-structure
Non-commutative fermion mass matrix and gravity
The first part is an introductory description of a small cross-section of the
literature on algebraic methods in non-perturbative quantum gravity with a
specific focus on viewing algebra as a laboratory in which to deepen
understanding of the nature of geometry. This helps to set the context for the
second part, in which we describe a new algebraic characterisation of the Dirac
operator in non-commutative geometry and then use it in a calculation on the
form of the fermion mass matrix. Assimilating and building on the various ideas
described in the first part, the final part consists of an outline of a
speculative perspective on (non-commutative) quantum spectral gravity. This is
the second of a pair of papers so far on this project.Comment: To appear in Int. J. Mod. Phys. A Previous title: An outlook on
quantum gravity from an algebraic perspective. 39 pages, 1 xy-pic figure,
LaTex Reasons for new version: added references, change of title and some
comments more up-to-dat
Weakly compact operators and the strong* topology for a Banach space
Peer reviewedPublisher PD
- …