8,213 research outputs found
The negative side of cohomology for Calabi-Yau categories
We study integer-graded cohomology rings defined over Calabi-Yau categories.
We show that the cohomology in negative degree is a trivial extension of the
cohomology ring in non-negative degree, provided the latter admits a regular
sequence of central elements of length two. In particular, the product of
elements of negative degrees are zero. As corollaries we apply this to
Tate-Hochschild cohomology rings of symmetric algebras, and to Tate cohomology
rings over group algebras. We also prove similar results for Tate cohomology
rings over commutative local Gorenstein rings.Comment: 14 page
Spectral Types of Field and Cluster O-Stars
The recent catalog of spectral types of Galactic O-type stars by
Mai'z-Apella'niz et al. has been used to study the differences between the
frequencies of various subtypes of O-type stars in the field, in OB
associations and among runaway stars. At a high level of statistical
significance the data show that O-stars in clusters and associations have
earlier types (and hence presumably larger masses and/or younger ages) than
those that are situated in the general field. Furthermore it is found that the
distribution of spectral subtypes among runaway O-stars is indistinguishable
from that among field stars, and differs significantly from that of the O-type
stars that are situated in clusters and associations. The difference is in the
sense that runaway O-stars, on average, have later subtypes than do those that
are still located in clusters and associations.Comment: To be published in the October 2004 issue of the Astronomical Journal
Included Figure 1, page
The Gorenstein defect category
We consider the homotopy category of complexes of projective modules over a
Noetherian ring. Truncation at degree zero induces a fully faithful triangle
functor from the totally acyclic complexes to the stable derived category. We
show that if the ring is either Artin or commutative Noetherian local, then the
functor is dense if and only if the ring is Gorenstein. Motivated by this, we
define the Gorenstein defect category of the ring, a category which in some
sense measures how far the ring is from being Gorenstein.Comment: 11 pages, updated versio
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