Graded algebras, polynomial identities and generic constructions

Eli Aljadeff

doi:10.1285/i15900932v34n1p1

Graded algebras, polynomial identities and generic constructions

Eli Aljadeff^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	1-21
Number of pages	21
Journal	Note di Matematica
Volume	34
Issue number	1
DOIs	https://doi.org/10.1285/i15900932v34n1p1
State	Published - 2014
Externally published	Yes

Keywords

Braucr group
Codimension growth
Division algebras
Group gradings
Polynomial identities

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year = "2014",

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AB - 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.

KW - Braucr group

KW - Codimension growth

KW - Division algebras

KW - Group gradings

KW - Polynomial identities

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Graded algebras, polynomial identities and generic constructions

Abstract

Keywords

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