We give an abstract version of the hard Lefschetz theorem, the Lefschetz decomposition and the Hodge–Riemann theorem for compact Kähler manifolds. Some examples are studied for compact symplectic Kähler manifolds.
"On the Lefschetz and Hodge–Riemann theorems." Illinois J. Math. 57 (1) 121 - 144, Spring 2013. https://doi.org/10.1215/ijm/1403534489