5,292 research outputs found
Gauss-Manin connections and Lie-Rinehart cohomology
In this note a generalized Gauss-Manin connection is constructed for
cohomology of Lie-Rinehart algebras, generalizing the classical Gauss-Manin
connection. As an application a Gysin-map between K-groups of flat connections
is constructed. We also calculate some examples of Gauss-Manin connections on
hypersurface singularities.Comment: Tha paper contained several mistakes and I chose to withdraw i
Lattice-ordered abelian groups and perfect MV-algebras: a topos-theoretic perspective
We establish, generalizing Di Nola and Lettieri's categorical equivalence, a
Morita-equivalence between the theory of lattice-ordered abelian groups and
that of perfect MV-algebras. Further, after observing that the two theories are
not bi-interpretable in the classical sense, we identify, by considering
appropriate topos-theoretic invariants on their common classifying topos, three
levels of bi-intepretability holding for particular classes of formulas:
irreducible formulas, geometric sentences and imaginaries. Lastly, by
investigating the classifying topos of the theory of perfect MV-algebras, we
obtain various results on its syntax and semantics also in relation to the
cartesian theory of the variety generated by Chang's MV-algebra, including a
concrete representation for the finitely presentable models of the latter
theory as finite products of finitely presentable perfect MV-algebras. Among
the results established on the way, we mention a Morita-equivalence between the
theory of lattice-ordered abelian groups and that of cancellative
lattice-ordered abelian monoids with bottom element.Comment: 54 page
The category of local algebras and points proches
Categorial methods for generating new local algebras from old ones are
presented. A direct proof of the differential structure of the prolongations of
a manifold is proposed
On derived equivalences of lines, rectangles and triangles
We present a method to construct new tilting complexes from existing ones
using tensor products, generalizing a result of Rickard. The endomorphism rings
of these complexes are generalized matrix rings that are "componentwise" tensor
products, allowing us to obtain many derived equivalences that have not been
observed by using previous techniques.
Particular examples include algebras generalizing the ADE-chain related to
singularity theory, incidence algebras of posets and certain Auslander algebras
or more generally endomorphism algebras of initial preprojective modules over
path algebras of quivers. Many of these algebras are fractionally Calabi-Yau
and we explicitly compute their CY dimensions. Among the quivers of these
algebras one can find shapes of lines, rectangles and triangles.Comment: v3: 21 pages. Slight revision, to appear in the Journal of the London
Mathematical Society; v2: 20 pages. Minor changes, pictures and references
adde
The Pimsner-Voiculescu sequence for coactions of compact Lie groups
The Pimsner-Voiculescu sequence is generalized to a Pimsner-Voiculescu tower
describing the -category equivariant with respect to coactions of a compact
Lie group satisfying the Hodgkin condition. A dual Pimsner-Voiculescu tower is
used to show that coactions of a compact Hodgkin-Lie group satisfy the
Baum-Connes property.Comment: 19 pages, to appear in Mathematica Scandinavic
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