28,480 research outputs found
Groups which do not admit ghosts
A ghost in the stable module category of a group G is a map between
representations of G that is invisible to Tate cohomology. We show that the
only non-trivial finite p-groups whose stable module categories have no
non-trivial ghosts are the cyclic groups of order 2 and 3. We compare this to
the situation in the derived category of a commutative ring. We also determine
for which groups G the second power of the Jacobson radical of kG is stably
isomorphic to a suspension of k.Comment: 9 pages, improved exposition and fixed several typos, to appear in
the Proceedings of the AM
The concept of social pharmacy
The 13th International Social Pharmacy Workshop will be held in Malta in July 2004. The Social Pharmacy Workshops are international conferences for research in social and behavioural pharmacy. Meetings are held every second year and participation has grown steadily since the first Workshop was held in Helsinki, Finland, in 1980. Following the successful 2002 conference in Sydney, Australia, the 2004 meeting in Malta will be the first one held in the Mediterranean area!peer-reviewe
The generating hypothesis for the stable module category of a -group
Freyd's generating hypothesis, interpreted in the stable module category of a
finite p-group G, is the statement that a map between finite-dimensional
kG-modules factors through a projective if the induced map on Tate cohomology
is trivial. We show that Freyd's generating hypothesis holds for a non-trivial
finite p-group G if and only if G is either C_2 or C_3. We also give various
conditions which are equivalent to the generating hypothesis.Comment: 6 pages, fixed minor typos, to appear in J. Algebr
Universality classes and crossover behaviors in non-Abelian directed sandpiles
We study universality classes and crossover behaviors in non-Abelian directed
sandpile models, in terms of the metastable pattern analysis. The non-Abelian
property induces spatially correlated metastable patterns, characterized by the
algebraic decay of the grain density along the propagation direction of an
avalanche. Crossover scaling behaviors are observed in the grain density due to
the interplay between the toppling randomness and the parity of the threshold
value. In the presence of such crossovers, we show that the broadness of the
grain distribution plays a crucial role in resolving the ambiguity of the
universality class. Finally, we claim that the metastable pattern analysis is
important as much as the conventional analysis of avalanche dynamics.Comment: 10 pages, 7 figures, 1 table; published in PRE as the full paper of
PRL v101, 218001 (2008
Transitions in non-conserving models of Self-Organized Criticality
We investigate a random--neighbours version of the two dimensional
non-conserving earthquake model of Olami, Feder and Christensen [Phys. Rev.
Lett. {\bf 68}, 1244 (1992)]. We show both analytically and numerically that
criticality can be expected even in the presence of dissipation. As the
critical level of conservation, , is approached, the cut--off of the
avalanche size distribution scales as . The
transition from non-SOC to SOC behaviour is controlled by the average branching
ratio of an avalanche, which can thus be regarded as an order
parameter of the system. The relevance of the results are discussed in
connection to the nearest-neighbours OFC model (in particular we analyse the
relevance of synchronization in the latter).Comment: 8 pages in latex format; 5 figures available upon reques
Ghosts in modular representation theory
A ghost over a finite p-group G is a map between modular representations of G
which is invisible in Tate cohomology. Motivated by the failure of the
generating hypothesis---the statement that ghosts between finite-dimensional
G-representations factor through a projective---we define the ghost number of
kG to be the smallest integer l such that the composition of any l ghosts
between finite-dimensional G-representations factors through a projective. In
this paper we study ghosts and the ghost numbers of p-groups. We begin by
showing that a weaker version of the generating hypothesis, where the target of
the ghost is fixed to be the trivial representation k, holds for all p-groups.
We then compute the ghost numbers of all cyclic p-groups and all abelian
2-groups with C_2 as a summand. We obtain bounds on the ghost numbers for
abelian p-groups and for all 2-groups which have a cyclic subgroup of index 2.
Using these bounds we determine the finite abelian groups which have ghost
number at most 2. Our methods involve techniques from group theory,
representation theory, triangulated category theory, and constructions
motivated from homotopy theory.Comment: 15 pages, final version, to appear in Advances in Mathematics. v4
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