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

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