More on quantum groups from the the quantization point of view

Star products on the classical double group of a simple Lie group and on corresponding symplectic grupoids are given so that the quantum double and the "quantized tangent bundle" are obtained in the deformation description. "Complex" quantum groups and bicovariant quantum Lie algebras are discused from this point of view. Further we discuss the quantization of the Poisson structure on symmetric algebra $S(g)$ leading to the quantized enveloping algebra $U_{h}(g)$ as an example of biquantization in the sense of Turaev. Description of $U_{h}(g)$ in terms of the generators of the bicovariant differential calculus on $F(G_q)$ is very convenient for this purpose. Finally we interpret in the deformation framework some well known properties of compact quantum groups as simple consequences of corresponding properties of classical compact Lie groups. An analogue of the classical Kirillov's universal character formula is given for the unitary irreducible representation in the compact case.Comment: 18 page

Antibacterial Resistance Leadership Group 2.0: Back to Business

In December 2019, the Antibacterial Resistance Leadership Group (ARLG) was awarded funding for another 7-year cycle to support a clinical research network on antibacterial resistance. ARLG 2.0 has 3 overarching research priorities: infections caused by antibiotic-resistant (AR) gram-negative bacteria, infections caused by AR gram-positive bacteria, and diagnostic tests to optimize use of antibiotics. To support the next generation of AR researchers, the ARLG offers 3 mentoring opportunities: the ARLG Fellowship, Early Stage Investigator seed grants, and the Trialists in Training Program. The purpose of this article is to update the scientific community on the progress made in the original funding period and to encourage submission of clinical research that addresses 1 or more of the research priority areas of ARLG 2.0

The complexity of equality constraint languages

Abstract. We apply the algebraic approach to infinite-valued constraint satisfaction to classify the computational complexity of all constraint satisfaction problems with templates that have a highly transitive automorphism group. A relational structure has such an automorphism group if and only if all the constraint types are Boolean combinations of the equality relation, and we call the corresponding constraint languages equality constraint languages. We show that an equality constraint language is tractable if it admits a constant unary or an injective binary polymorphism, and is NP-complete otherwise