Groups and noncommutative algebra: interactions and applications
Introduction to cyclic codes over commutative rings and algebraic integer numbers ...
Introduction to finite fields and to algebraic error-correcting codes
Abstract
We intend to continue the research on non commutative algebra. In particular, we wish to study the interactions between Group theory and the Theory of Rings and Algebras, as well as some of its applications, especially, to partial actions of groups on rings and to the Theory of Error-correcting Codes. Our group has worked on these directions for quite some time in the past and has already obtained results that are frequently quoted in the literature. Specific subjects to be studied in the period are, among others:* The structure of group algebras, considered as rings with involution and the group of units of a group ring.* The structure of the group of units of a division ring and the existence of free pairs of special type.* Study of globalization of partial actions, generalized crossed products, isomorphism of partial group algebras, partial actions and co-actions of Hopf algebras, partial projective representations and co-homology based on partial actions.* The study of error-correcting codes, defined from groups. In particular, we expect to study the relations among different classes of codes - cyclic, abelian, metacyclic, etc. - using techniques of finite group algebras. (AU)
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