Graded algebras, polynomial identities and generic constructions

Eli Aljadeff*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In these lecture we present some results which intertwine topics as graded algebras, polynomial identities and algebras of generic elements. Some of these connections arc classical and well known to different communities (e.g. crossed products, Galois cohomology, algebra of generic matrices, general group gradings on finite dimensional algebra). Some other connections among these topics arc relatively new where these arc realized via the theory of group graded polynomial identities. In particular, using (G-gradcd) asymptotic PI theory, we outline the proof of a conjecture of Bahturin and Rcgcv on regular gradings on associative algebras. These lectures took place in Porto Ccsarco, Italy. The author is mostly grateful to the organizers of the meeting Advances in Group theory.

Original languageEnglish
Pages (from-to)1-21
Number of pages21
JournalNote di Matematica
Volume34
Issue number1
DOIs
StatePublished - 2014
Externally publishedYes

Keywords

  • Braucr group
  • Codimension growth
  • Division algebras
  • Group gradings
  • Polynomial identities

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