M.Sc Thesis
M.Sc Student David Ofir On Regular Gradings of Algebras Department of Mathematics Professor Eli Aljadeff

Abstract

Let G be a finite abelian group and A a G-graded algebra over a field F. The G-grading is called regular with commutation function θ: G?G→F?, if for any sequence (g1,?,gn) in Gn  there are ai homogeneous of degree gi such that a1*a2*?*an ≠0 , and for any ag, bh of degrees g and h respectively we have ag*bh = θ(g,h) bh*ag.

Each such function θ must also be a skew symmetric bicharacter, meaning that for any g, h in G we have θ(g,h) = θ(h,g)-1, and for fixed h in G the maps g→θ(h,g) and g→θ(g,h) are characters on G.

A regular grading is called minimal (and θ is called non-degenerate) if for any e≠g in G there is some h in G such that θ(g,h)≠1.