The Poisson center and polynomial, maximal Poisson commutative subalgebras, especially for nilpotent Lie algebras of dimension at most seven

Let g be a finite dimensional Lie algebra over an algebraically closed field k of characteristic zero. We collect some general results on the Poisson center of S(g), including some simple criteria regarding its polynomiality, and also on certain Poisson commutative subalgebras of S(g). These facts are then used to finish our earlier work on this subject, i.e. to give an explicit description for the Poisson center of all indecomposable, nilpotent Lie algebras of dimension at most seven. Among other things, we also provide a polynomial, maximal Poisson commutative subalgebra of S(g), enjoying additional properties. As a by-product we show that a conjecture by Milovanov is valid in this situation. These results easily carry over to the enveloping algebra U(g).Comment: 48 page

On Commutative Polarizations

The purpose of this paper is to study finite-dimensional Lie algebras over a field k of characteristic zero which admit a commutative polarization (CP). Among the many results and examples, it is shown that, if k is algebraically closed, the nilradical N of a parabolic subalgebra in A_n and C_n has such a CP. Using this fact a simple closed formula is derived for the index of N.Comment: 34 pages, 2 figures. Submitted to Journal of Algebr

Structural basis of template-boundary definition in Tetrahymena telomerase.

Telomerase is required to maintain repetitive G-rich telomeric DNA sequences at chromosome ends. To do so, the telomerase reverse transcriptase (TERT) subunit reiteratively uses a small region of the integral telomerase RNA (TER) as a template. An essential feature of telomerase catalysis is the strict definition of the template boundary to determine the precise TER nucleotides to be reverse transcribed by TERT. We report the 3-Å crystal structure of the Tetrahymena TERT RNA-binding domain (tTRBD) bound to the template boundary element (TBE) of TER. tTRBD is wedged into the base of the TBE RNA stem-loop, and each of the flanking RNA strands wraps around opposite sides of the protein domain. The structure illustrates how the tTRBD establishes the template boundary by positioning the TBE at the correct distance from the TERT active site to prohibit copying of nontemplate nucleotides

Insights in a restricted temporary pacemaker strategy in a lean transcatheter aortic valve implantation program

OBJECTIVES: To study the safety and feasibility of a restrictive temporary‐RV‐pacemaker use and to evaluate the need for temporary pacemaker insertion for failed left ventricular (LV) pacing ability (no ventricular capture) or occurrence of high‐degree AV‐blocks mandating continuous pacing. BACKGROUND: Ventricular pacing remains an essential part of contemporary transcatheter aortic valve implantation (TAVI). A temporary‐right‐ventricle (RV)‐pacemaker lead is the standard approach for transient pacing during TAVI but requires central venous access. METHODS: An observational registry including 672 patients who underwent TAVI between June 2018 and December 2020. Patients received pacing on the wire when necessary, unless there was a high‐anticipated risk for conduction disturbances post‐TAVI, based on the baseline‐ECG. The follow‐up period was 30 days. RESULTS: A temporary‐RV‐pacemaker lead (RVP‐cohort) was inserted in 45 patients, pacing on the wire (LVP‐cohort) in 488 patients, and no pacing (NoP‐cohort) in 139 patients. A bailout temporary pacemaker was implanted in 14 patients (10.1%) in the NoP‐cohort and in 24 patients (4.9%) in the LVP‐cohort. One patient in the LVP‐cohort needed an RV‐pacemaker for incomplete ventricular capture. Procedure time was significantly longer in the RVP‐cohort (68 min [IQR 52–88.] vs. 55 min [IQR 44–72] in NoP‐cohort and 55 min [IQR 43–71] in the LVP‐cohort [p < 0.005]). Procedural high‐degree AV‐block occurred most often in the RVP‐cohort (45% vs. 14% in the LVP and 16% in the NoP‐cohort [p ≤ 0.001]). Need for new PPI occurred in 47% in the RVP‐cohort, versus 20% in the NoP‐cohort and 11% in the LVP‐cohort (p ≤ 0.001). CONCLUSION: A restricted RV‐pacemaker strategy is safe and shortens procedure time. The majority of TAVI‐procedures do not require a temporary‐RV‐pacemaker

Modular Lie algebras and the Gelfand-Kirillov conjecture

Let g be a finite dimensional simple Lie algebra over an algebraically closed field of characteristic zero. We show that if the Gelfand-Kirillov conjecture holds for g, then g has type A_n, C_n or G_2.Comment: 20 page