[en] In this paper, working over an algebraically closed field k of prime characteristic p, we introduce a concept, called Primitive Deformation, to provide a structured technique to classify certain finite-dimensional Hopf algebras which are Hopf deformations of restricted universal enveloping algebras. We illustrate this technique for the case when the restricted Lie algebra has dimension 3. Together with our previous classification results, we provide a complete classification of p³-dimensional connected Hopf algebras over k of characteristic p > 2.

[en] A theory of itinerant ferromagnetism in superconducting semimetals is proposed. A nonzero mean magnetisation appears in the superconducting state due to the interaction (interference) of spin density wave (SDW), charge density wave (CDW) and Cooper pair wave. Phase diagram and physical properties of the states considered are investigated analytically and numerically. (orig.)

[en] We study which algebras have tilting modules that are both generated and cogenerated by projective–injective modules. Crawley–Boevey and Sauter have shown that Auslander algebras have such tilting modules; and for algebras of global dimension 2, Auslander algebras are classified by the existence of such tilting modules. In this paper, we show that the existence of such a tilting module is equivalent to the algebra having dominant dimension at least 2, independent of its global dimension. In general such a tilting module is not necessarily cotilting. Here, we show that the algebras which have a tilting–cotilting module generated–cogenerated by projective–injective modules are precisely 1-minimal Auslander–Gorenstein algebras. When considering such a tilting module, without the assumption that it is cotilting, we study the global dimension of its endomorphism algebra, and discuss a connection with the Finitistic Dimension Conjecture. Furthermore, as special cases, we show that triangular matrix algebras obtained from Auslander algebras and certain injective modules, have such a tilting module. We also give a description of which Nakayama algebras have such a tilting module.