Classification of the finite dimensional absolute valued algebras having a non-zero central idempotent or a one-sided unity

An absolute valued algebra is a non-zero real algebra that is equipped with a multiplicative norm. We classify all finite dimensional absolute valued algebras having a non-zero central idempotent or a one-sided unity, up to algebra isomorphism. This completes earlier results of Ramírez Álvarez and Rochdi which, in our self-contained presentation, are recovered from the wider context of composition k-algebras with an LR-bijective idempotent.     

Laurent phenomenon sequences

In this paper, we undertake a systematic study of sequences generated by recurrences \(x_{m+n}x_m = P(x_{m+1}, \ldots , x_{m+n-1})\) which exhibit the Laurent phenomenon. Some of the most famous among these are the Somos and the Gale-Robinson sequences. Our approach is based on finding period 1 seeds of Laurent phenomenon algebras of Lam–Pylyavskyy. We completely classify polynomials P that generate period 1 seeds in the cases of \(n=2,3\) and of mutual binomial seeds. We also find several other interesting families of polynomials P whose generated sequences exhibit the Laurent phenomenon. Our classification for binomial seeds is a direct generalization of a result by Fordy and Marsh, that employs a new combinatorial gadget we call a double quiver.     

Synthesis and structural characterization of novel tetranuclear organotitanoxane derivatives

Synthesis of the novel titanoxane compounds, [(TiCl)(TiOH){(Ti)[μ-(η(5)-C(5)Me(4)SiMe(2)O-κO)](2)(μ-O)}(2)(μ-O)] (4) and [{Ti[μ-(η(5)-C(5)Me(4)SiMe(2)O-κO)](μ-O)}(4)] (5) by controlled reaction of the dinuclear titanium oxo complex [{Ti{μ-(η(5)-C(5)Me(4)SiMe(2)O-κO)}Cl](2)(μ-O)] (1) with 2 equiv of LiOH is reported. Complex 4 is innovative and remarkable. It is one of the rare known examples of tetranuclear stable terminal hydroxo titanium complexes, with an open-chained structure, which coincides with the transient metal monohydroxo proposed in the stepwise pathway employed to justify the formation of the hexanuclear complex [{Ti[μ-(η(5)-C(5)Me(4)SiMe(2)O-κO)](μ-O)}(6)] (3) from 1. (1)H DOSY experiments were used to characterize complex 4. In addition, the structures of compound 5 and of precursor 1 were determined by single-crystal X-ray diffraction studies.     

Competitive Gold‐Activation Modes in Terminal Alkynes: An Experimental and Mechanistic Study

The competition between π‐ and dual σ,π‐gold‐activation modes is revealed in the gold(I)‐catalyzed heterocyclization of 1‐(o‐ethynylaryl)urea. A noticeable effect of various ligands in gold complexes on the choice of these activation modes is described. The cationic [Au(IPr)]⁺ (IPr=2,6‐bis(diisopropylphenyl)imidazol‐2‐ylidene) complex cleanly promotes the π activation of terminal alkynes, whereas [Au(PtBu₃)]⁺ favors intermediate σ,π species. In this experimental and mechanistic study, which includes kinetic and cross‐over experiments, several σ‐gold, σ,π‐gold, and other gold polynuclear reaction intermediates have been isolated and identified by NMR spectroscopy, X‐ray diffraction, or MALDI spectrometry. The ligand control in the simultaneous or alternative π‐ and σ,π‐activation modes is also supported by deuterium‐labeling experiments.     

Undeniable Confirmation of the syn‐Addition Mechanism for Metal‐Free Diboration by Using the Crystalline Sponge Method

The stereochemical outcome of the recently developed metal‐free 1,2‐diboration of aliphatic alkenes has, until now, only been elucidated by indirect means (e.g. derivatization). This is because classical conformational analysis of the resulting 1,2‐diboranes is not viable; in the ¹H NMR spectrum the relevant ¹H resonances are broadened by ¹¹B, and the occurrence of the products as oily compounds precludes X‐ray crystallographic analysis. Herein, the crystalline sponge method is used to display the crystal structures of the diboronic esters formed from internal E and Z olefins, evidencing the stereospecific syn addition mechanism of the reaction, which is fully consistent with the prediction from DFT calculations.     

Efficient Synthesis of (−)‐(R)‐Muscone by Enantioselective Protonation

A new synthesis of (?)‐(R)‐muscone ((R)‐ 1 ) by means of enantioselective protonation of a bicyclic ketone enolate as the key step (see 6 →(S)‐ 4 in Scheme 2) is presented. The C₁₅ macrocyclic system is obtained by ozonolysis (Scheme 7).     

Synthesis and characterization of manganese(II) and iron(III) d5 tripodal imidazole complexes. Effect of oxidation state, protonation state and ligand conformation on coordination number and spin state

The 1 : 3 Schiff base condensates of tris(2-aminoethyl)amine (tren) or tris(3-aminopropyl)amine (trpn) with 4-methyl-5-imidazolecarboxaldehyde, H3L1 and H3L2, respectively, were generated in situ and used to prepare complexes with manganese(II) and iron(III). The resultant complexes, [MnH3L1](ClO4)2, [MnH3L1](ClO4)2.EtOH.H2O, [MnH3L2](ClO4)2, [FeH3L1](ClO4)3.1.5(EtOH) and [FeHL1](I3) (0.525)(I)(0.475).2.625H2O, have been characterized by EA, IR, ES MS, variable temperature magnetic susceptibility, X-ray crystallography, and M?ssbauer spectroscopy for the iron complexes. The three manganese(II) complexes are high spin with [MnH3L2](ClO4)2 exhibiting coordination number seven while the others are six coordinate. [FeH3L1](ClO4)3.1.5(EtOH) has two iron sites, a seven coordinate and a pseudo seven coordinate site. The complex is high spin at room temperature but exhibits a magnetic moment that decreases with temperature corresponding to conversion of one of the sites to low spin. [FeHL1](I3) (0.525)(I)(0.475).2.625H2O is low spin even at room temperature. In the present complexes the apical nitrogen atom, N(ap), of the tripodal ligand is pyramidal and directed toward the metal atom. The data show that the M-N(ap) distance decreases as the oxidation state of the metal increases, as the number of bound imidazole protons on the ligand increases, and as the number of carbon atoms in the backbone of the ligand (tren vs. trpn) increases. In a limiting sense, short M-N(ap) distances result in high spin seven coordinate mono capped octahedral complexes and long M-N(ap) distances result in low spin six coordinate octahedral complexes.     

The Power of Iodane-Guided C−H Coupling: A Group-Transfer Strategy in Which a Halogen Works for Its Money

Hypervalent organoiodane reagents are ubiquitous in organic synthesis, both as oxidants and as electrophilic group-transfer agents. In addition to these hallmark applications, a complementary strategy is gaining momentum that exploits the ability of λ³-iodanes to undergo iodine-to-arene group transfer, for example, via iodonio-Claisen-type rearrangement processes. This Minireview discusses recent advances in the use of this method to access a variety of the C−H-functionalized iodoarenes. While Section 2 is focused on the ortho C−H propargylation, allylation, and the more unusual para C−H benzylation, Section 3 is devoted to the C-arylation of enol and phenol substrates. The accompanying discussion includes mechanistic considerations and goes into the synthetic applications of the final iodoarene cores. The Minireview concludes with further conceptual extensions of the method, including the use of non-conventional coupling partners (for example, cyanoalkylation), improved access to λ³-iodane building blocks, and the development of iterative approaches to polysubstituted iodoarenes.