立命館大学数理科学科

We consider a class of 2 step nilpotent Lie algebras which are  attached to a class of Clifford modules. We call them pseudo H-type algebras. They are a generalization of Heisenberg algebra. First we show the existence of integral lattices and explain how we classify them. Then we determine all the cases of their automorphism groups. Many properties of this algebra reduce to 49 basic cases by three periodicities, so called Bott periodicity. Finally I will  discuss about the uniqueness of the integral lattice.