147,437 research outputs found
-abelian and -exact categories
We introduce -abelian and -exact categories, these are analogs of
abelian and exact categories from the point of view of higher homological
algebra. We show that -cluster-tilting subcategories of abelian (resp.
exact) categories are -abelian (resp. -exact). These results allow to
construct several examples of -abelian and -exact categories. Conversely,
we prove that -abelian categories satisfying certain mild assumptions can be
realized as -cluster-tilting subcategories of abelian categories. In analogy
with a classical result of Happel, we show that the stable category of a
Frobenius -exact category has a natural -angulated structure in the
sense of Gei\ss-Keller-Oppermann. We give several examples of -abelian and
-exact categories which have appeared in representation theory, commutative
ring theory, commutative and non-commutative algebraic geometry.Comment: 58 pages. Corrected an error in Thm 3.20 and Lemma 3.22 and several
typos. Accepted for publication in Mathematische Zeitschrif
Site selectivity of halogen oxygen bonding in 5- and 6-haloderivatives of uracil
Seven 5-and 6-halogenated derivatives of uracil or 1-methyluracil (halogen = Cl, Br, I) were
studied by single crystal X-ray diffraction. In contrast with pure 5-halouracils, where the presence
of N-H…O and C-H…O hydrogen bonds prevents the formation of other intermolecular interactions,
the general ability of pyrimidine nucleobases to provide electron donating groups to halogen
bonding was confirmed in three crystals and cocrystals containing uracil with the halogen atom at
the C6 position. In the latter compounds, among the two nucleophilic oxygen atoms in the C=O
moiety, only the urea carbonyl oxygen O1 can act as halogen bond acceptor, being not saturated by
conventional hydrogen bonds. The halogen bonds in pure 6-halouracils are all rather weak, as
supported by Hirshfeld surface analysis. The strongest interaction was found in the structure of 6-
iodouracil, which displayed the largest (13%) reduction of the sum of van der Waals (vdW) radii for
the contact atoms. Despite this, halogen bonding plays a rol
Higher Auslander algebras of type and the higher Waldhausen -constructions
These notes are an expanded version of my talk at the ICRA 2018 in Prague,
Czech Republic; they are based on joint work with Tobias Dyckerhoff and Tashi
Walde. In them we relate Iyama's higher Auslander algebras of type
to Eilenberg--Mac Lane spaces in algebraic topology and to higher-dimensional
versions of the Waldhausen -construction from algebraic
-theory.Comment: 16 pages. The author's contribution to the Proceedings of the ICRA
2018, v.2 minor edits following referee repor
Equilibrium Fluctuations for a One-Dimensional Interface in the Solid on Solid Approximation
An unbounded one-dimensional solid-on-solid model with integer heights is
studied. Unbounded here means that there is no a priori restrictions on the
discret e gradient of the interface. The interaction Hamiltonian of the
interface is given by a finite range part, pr oportional to the sum of height
differences, plus a part of exponentially decaying long range potentials. The
evolution of the interface is a reversible Markov process. We prove that if
this system is started in the center of a box of size L after a time of order
L^3 it reaches, with a very large probability, the top or the bottom of the
box
Black hole nonmodal linear stability: the Schwarzschild (A)dS cases
The nonmodal linear stability of the Schwarzschild black hole established in
Phys. Rev. Lett. 112 (2014) 191101 is generalized to the case of a nonnegative
cosmological constant . Two gauge invariant combinations of
perturbed scalars made out of the Weyl tensor and its first covariant
derivative are found such that the map
with domain the set of equivalent classes under gauge
transformations of solutions of the linearized Einstein's equation, is
invertible. The way to reconstruct a representative of in
terms of is given. It is proved that, for an arbitrary perturbation
consistent with the background asymptote, and are bounded in the
the outer static region. At large times, the perturbation decays leaving a
linearized Kerr black hole around the Schwarzschild or Schwarschild de Sitter
background solution. For negative cosmological constant it is shown that there
is a choice of boundary conditions at the time-like boundary under which the
Schwarzschild anti de Sitter black hole is unstable. The root of
Chandrasekhar's duality relating odd and even modes is exhibited, and some
technicalities related to this duality and omitted in the original proof of the
case are explained in detail.Comment: Typos corrected, changes in the Introduction (including example of
nonmodal instability
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