9 research outputs found
Cohomological Donaldson-Thomas theory of a quiver with potential and quantum enveloping algebras
This paper concerns the cohomological aspects of Donaldson-Thomas theory for
Jacobi algebras and the associated cohomological Hall algebra, introduced by
Kontsevich and Soibelman. We prove the Hodge-theoretic categorification of the
integrality conjecture and the wall crossing formula, and furthermore realise
the isomorphism in both of these theorems as Poincar\'e-Birkhoff-Witt
isomorphisms for the associated cohomological Hall algebra. We do this by
defining a perverse filtration on the cohomological Hall algebra, a result of
the "hidden properness" of the semisimplification map from the moduli stack of
semistable representations of the Jacobi algebra to the coarse moduli space of
polystable representations. This enables us to construct a degeneration of the
cohomological Hall algebra, for generic stability condition and fixed slope, to
a free supercommutative algebra generated by a mixed Hodge structure
categorifying the BPS invariants. As a corollary of this construction we
furthermore obtain a Lie algebra structure on this mixed Hodge structure - the
Lie algebra of BPS invariants - for which the entire cohomological Hall algebra
can be seen as the positive part of a Yangian-type quantum group.Comment: v5 final version, 64 pages, to appear in Invent. Math. Many thanks to
the anonymous referee for helpful suggestion
Regulating the Size and Stabilization of Lipid Raft-like Domains and Using Calcium Ions as Their Probe
Inhibiting Lateral Domain Formation in Lipid Bilayers: Simulations of Alternative Steroid Headgroup Chemistries
Antibody-induced and cytoskeleton-mediated redistribution and shedding of viral glycoproteins, expressed on pseudorabies virus-infected cells
Polylysine-Induced 2H NMR-Observable Domains in Phosphatidylserine/Phosphatidylcholine Lipid Bilayers
Statistical Convergence of Equilibrium Properties in Simulations of Molecular Solutes Embedded in Lipid Bilayers
An intercalation mechanism as a mode of action exerted by psychotropic drugs: results of altered phospholipid substrate availabilities in membranes?
Patients respond differently to psychotropic drugs, and this is currently a controversial theme among psychiatrists. The effects of 16 psychotropics on cell membrane parameters have been reported. These drugs belong to three major groups used in therapeutic psychiatry: antipsychotics, antidepressants, and anxiolytic/hypnotics. Human platelets, lacking dopamine (D2) receptors (proposed targets of most psychotropics), have been used as a cell model. Here we discuss the effects of these drugs on three metabolic phenomena and also results from Langmuir experiments. Diazepam, in contrast to the remaining drugs, had negligible effects on metabolic phenomena and had no effects in Langmuir experiments. Psychotropic drugs may work through intercalation in membrane phospholipids. It is possible that the fluidity of membranes, rich in essential fatty acids, the content being influenced by diet, could be a contributing factor to the action of psychotropics. This might in turn explain the observed major differences in therapeutic response among patients