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 language | English |
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Pages (from-to) | 1-21 |
Number of pages | 21 |
Journal | Note di Matematica |
Volume | 34 |
Issue number | 1 |
DOIs | |
State | Published - 2014 |
Externally published | Yes |
Keywords
- Braucr group
- Codimension growth
- Division algebras
- Group gradings
- Polynomial identities