Descent, fields of invariants, and generic forms via symmetric monoidal categories

Research output: Contribution to journalArticle

1 Citation (Scopus)
5 Downloads (Pure)

Abstract

Let W be a finite dimensional algebraic structure (e.g. an algebra) over a field K of characteristic zero. We study forms of W by using Deligne's Theory of symmetric monoidal categories. We construct a category CW, which gives rise to a subfield K0⊆K, which we call the field of invariants of W. This field will be contained in any subfield of K over which W has a form. The category CW is a K0-form of RepK¯(Aut(W)), and we use it to construct a generic form W˜ over a commutative K0-algebra BW (so that forms of W are exactly the specializations of W˜). This generalizes some generic constructions for central simple algebras and for H-comodule algebras. We give some concrete examples arising from associative algebras and H-comodule algebras. As an application, we also explain how one can use the construction to classify two-cocycles on some finite dimensional Hopf algebras.
Original languageEnglish
Pages (from-to)2077-2111
Number of pages35
JournalJournal of Pure and Applied Algebra
Volume220
Issue number6
Early online date10 Nov 2015
DOIs
Publication statusPublished - Jun 2016

Fingerprint Dive into the research topics of 'Descent, fields of invariants, and generic forms via symmetric monoidal categories'. Together they form a unique fingerprint.

  • Cite this