AUTOMORPHISMS OF ALGEBRAS AND ORTHOGONAL POLYNOMIALS

Suitable automorphisms together with complete classification of representations of some algebras can be used to generate some sets of orthogonal polynomials “at no cost”. This is also the case of nonstandard Klimyk-Gavrilik deformation Uq'(so3) which is connected to q-Racah polynomials

Borohydrido rare earth complexes as precatalysts for the polymerisation of styrene

Borohydrido based lanthanide complexes associated with n-butylethylmagnesium are efficient catalytic systems for the polymerisation of styrene. The reaction is quantitative at 50°C after several hours. Two growing chains per magnesium atom can be evidenced, and chain transfer between the lanthanide and the magnesium atoms may occur. The activity of such catalytic systems is found to be related to the nature of the rare earth

Group-theoretical graph categories

The semidirect product of a finitely generated group dual with the symmetric group can be described through so-called group-theoretical categories of partitions (covers only a special case; due to Raum--Weber, 2015) and skew categories of partitions (more general; due to Maassen, 2018). We generalize these results to the case of graph categories, which allows to replace the symmetric group by the group of automorphisms of some graph.Comment: 32 pages; changes: removed former Section 4.4 (as superfluous), modified formulation of Thm. B, made some additional minor changes and correction

Gluing Compact Matrix Quantum Groups

We study glued tensor and free products of compact matrix quantum groups with cyclic groups – so-called tensor and free complexifications. We characterize them by studying their representation categories and algebraic relations. In addition, we generalize the concepts of global colourization and alternating colourings from easy quantum groups to arbitrary compact matrix quantum groups. Those concepts are closely related to tensor and free complexification procedures. Finally, we also study a more general procedure of gluing and ungluing

Gluing Compact Matrix Quantum Groups

We study glued tensor and free products of compact matrix quantum groups with cyclic groups – so-called tensor and free complexifications. We characterize them by studying their representation categories and algebraic relations. In addition, we generalize the concepts of global colourization and alternating colourings from easy quantum groups to arbitrary compact matrix quantum groups. Those concepts are closely related to tensor and free complexification procedures. Finally, we also study a more general procedure of gluing and ungluing