Finite Subgroups of Units in Integral Group Rings

This is a short survey in which some questions related to the Zassenhaus Conjecture on finite subgroups in integral group rings are discussed . The bibliography is incomplete but gives a possibility to surch for more references and to find out the details of the subject development

Twisted partial actions of Hopf algebras

In this work, the notion of a twisted partial Hopf action is introduced as a unified approach for twisted partial group actions, partial Hopf actions and twisted actions of Hopf algebras. The conditions on partial cocycles are established in order to construct partial crossed products, which are also related to partially cleft extensions of algebras. Examples are elaborated using algebraic groups

Dynkin diagrams and spectra of graphs

Dynkin diagrams rst appeared in [20] in the connection with classication of simple Lie groups. Among Dynkin diagrams a special role is played by the simply laced Dynkin diagrams An, Dn, E6, E7 and E8. Dynkin diagrams are closely related to Coxeter graphs that appeared in geometry (see [8]). After that Dynkin diagrams appeared in many braches of mathematics and beyond, em particular em representation theory

On spectra of abelian group rings

In this paper we study the spectrum of integral group rings of finitely generated abelian groups G from the scheme-theoretic viewpoint. We prove that the (closed) singular points of Spec Z[G], the (closed) intersection points of the irreducible components of Spec Z[G] and the (closed) points over the prime divisors of vertical bar t(G)vertical bar coincide. We also determine the formal completion of Spec Z[G] at a singular point

Group algebras whose involutory units commute

Consiglio Nazionale delle Ricerche - Biblioteca Centrale - P.le Aldo Moro, 7 Rome / CNR - Consiglio Nazionale delle RichercheSIGLEITItal