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 K0form of RepK¯(Aut(W)), and we use it to construct a generic form W˜ over a commutative K0algebra BW (so that forms of W are exactly the specializations of W˜). This generalizes some generic constructions for central simple algebras and for Hcomodule algebras. We give some concrete examples arising from associative algebras and Hcomodule algebras. As an application, we also explain how one can use the construction to classify twococycles on some finite dimensional Hopf algebras.
Original language  English 

Pages (fromto)  20772111 
Number of pages  35 
Journal  Journal of Pure and Applied Algebra 
Volume  220 
Issue number  6 
Early online date  10 Nov 2015 
DOIs  
Publication status  Published  Jun 2016 
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Ehud Meir Ben Efraim
 School of Natural & Computing Sciences, Mathematical Science  Senior Lecturer
Person: Academic