The quantum duality principle

The "quantum duality principle" states that the quantization of a Lie bialgebra - via a quantum universal enveloping algebra (QUEA) - provides also a quantization of the dual Lie bialgebra (through its associated formal Poisson group) - via a quantum formal series Hopf algebra (QFSHA) - and, conversely, a QFSHA associated to a Lie bialgebra (via its associated formal Poisson group) yields a QUEA for the dual Lie bialgebra as well; more precisely, there exist functors QUEA --> QFSHA and QFSHA --> QUEA, inverse of each other, such that in either case the Lie bialgebra associated to the target object is the dual of that of the source object. Such a result was claimed true by Drinfeld, but seems to be unproved in literature: we give here a complete detailed proof of it.Comment: 19 pages, AMS-TeX file. The paper has been entirely re-written: in particular, we add a discussion of the possible generalisation of the main result to the infinite dimensional case. This is the author's file of the final version (after the refereeing process), as sent for publicatio

Quantum function algebras as quantum enveloping algebras

Inspired by a result in [Ga], we locate two $k[q,q^{-1}]$-integer forms of $F_q[SL(n+1)]$, along with a presentation by generators and relations, and prove that for $q=1$ they specialize to $U({\mathfrak{h}})$, where ${\mathfrak{h}}$ is the Lie bialgebra of the Poisson Lie group $H$ dual of $SL(n+1)$; moreover, we explain the relation with [loc. cit.]. In sight of this, we prove two PBW-like theorems for $F_q[SL(n+1)]$, both related to the classical PBW theorem for $U({\mathfrak{h}})$.Comment: 27 pages, AMS-TeX C, Version 3.0 - Author's file of the final version, as it appears in the journal printed version, BUT for a formula in Subsec. 3.5 and one in Subsec. 5.2 - six lines after (5.1) - that in this very pre(post)print have been correcte

A quantum homogeneous space of nilpotent matrices

A quantum deformation of the adjoint action of the special linear group on the variety of nilpotent matrices is introduced. New non-embedded quantum homogeneous spaces are obtained related to certain maximal coadjoint orbits, and known quantum homogeneous spaces are revisited.Comment: 12 page

Test, Reliability and Functional Safety Trends for Automotive System-on-Chip

This paper encompasses three contributions by industry professionals and university researchers. The contributions describe different trends in automotive products, including both manufacturing test and run-time reliability strategies. The subjects considered in this session deal with critical factors, from optimizing the final test before shipment to market to in-field reliability during operative life

A 2-categorical extension of Etingof–Kazhdan quantisation

Let k be a field of characteristic zero. Etingof and Kazhdan constructed a quantisation U_h(b) of any Lie bialgebra b over k, which depends on the choice of an associator Phi. They prove moreover that this quantisation is functorial in b. Remarkably, the quantum group U_h(b) is endowed with a Tannakian equivalence F_b from the braided tensor category of Drinfeld-Yetter modules over b, with deformed associativity constraints given by Phi, to that of Drinfeld-Yetter modules over U_h(b). In this paper, we prove that the equivalence F_b is functorial in b.Comment: Small revisions in Sections 2 and 6. An appendix added on the equivalence between admissible Drinfeld-Yetter modules over a QUE and modules over its quantum double. To appear in Selecta Math. 71 page

A short history of the 5-HT2C receptor: from the choroid plexus to depression, obesity and addiction treatment

This paper is a personal account on the discovery and characterization of the 5-HT2C receptor (first known as the 5- HT1C receptor) over 30 years ago and how it translated into a number of unsuspected features for a G protein-coupled receptor (GPCR) and a diversity of clinical applications. The 5-HT2C receptor is one of the most intriguing members of the GPCR superfamily. Initially referred to as 5-HT1CR, the 5-HT2CR was discovered while studying the pharmacological features and the distribution of [3H]mesulergine-labelled sites, primarily in the brain using radioligand binding and slice autoradiography. Mesulergine (SDZ CU-085), was, at the time, best defined as a ligand with serotonergic and dopaminergic properties. Autoradiographic studies showed remarkably strong [3H]mesulergine-labelling to the rat choroid plexus. [3H]mesulergine-labelled sites had pharmacological properties different from, at the time, known or purported 5-HT receptors. In spite of similarities with 5-HT2 binding, the new binding site was called 5-HT1C because of its very high affinity for 5-HT itself. Within the following 10 years, the 5-HT1CR (later named 5- HT2C) was extensively characterised pharmacologically, anatomically and functionally: it was one of the first 5-HT receptors to be sequenced and cloned. The 5-HT2CR is a GPCR, with a very complex gene structure. It constitutes a rarity in theGPCR family: many 5-HT2CR variants exist, especially in humans, due to RNA editing, in addition to a few 5-HT2CR splice variants. Intense research led to therapeutically active 5-HT2C receptor ligands, both antagonists (or inverse agonists) and agonists: keeping in mind that a number of antidepressants and antipsychotics are 5- HT2CR antagonists/inverse agonists. Agomelatine, a 5-HT2CR antagonist is registered for the treatment of major depression. The agonist Lorcaserin is registered for the treatment of aspects of obesity and has further potential in addiction, especially nicotine/ smoking. There is good evidence that the 5-HT2CR is involved in spinal cord injury-induced spasms of the lower limbs, which can be treated with 5-HT2CR antagonists/inverse agonists such as cyproheptadine or SB206553. The 5-HT2CR may play a role in schizophrenia and epilepsy. Vabicaserin, a 5-HT2CR agonist has been in development for the treatment of schizophrenia and obesity, but was stopped. As is common, there is potential for further indications for 5-HT2CR ligands, as suggested by a number of preclinical and/or genome-wide association studies (GWAS) on depression, suicide, sexual dysfunction, addictions and obesity. The 5-HT2CR is clearly affected by a number of established antidepressants/antipsychotics and may be one of the culprits in antipsychotic-induced weight gain

A multi-element psychosocial intervention for early psychosis (GET UP PIANO TRIAL) conducted in a catchment area of 10 million inhabitants: study protocol for a pragmatic cluster randomized controlled trial

Multi-element interventions for first-episode psychosis (FEP) are promising, but have mostly been conducted in non-epidemiologically representative samples, thereby raising the risk of underestimating the complexities involved in treating FEP in 'real-world' services