The Hodge group of a rational Hodge structure 
is the smallest algebraic subgroup
of GL(V) over 
whose real points contain its Hodge circle. For a fixed weight, the multiplicative
characters 
of the Hodge circle on 
distinguish the Hodge types (Huybrechts 2016).
Hodge Group
See also
Algebraic Group, Hodge Circle, Hodge Cycle, Hodge Structure, Kuga-Satake CorrespondenceExplore with Wolfram|Alpha
References
Huybrechts, D. Lectures on K3 Surfaces. Cambridge, England: Cambridge University Press, 2016. https://doi.org/10.1017/CBO9781316594193.Cite this as:
Weisstein, Eric W. "Hodge Group." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/HodgeGroup.html