模代数的形变理论

A Theory of Deformations of Module Algebras

本文构作了与模代数HA相适应的“形变复形”CH*(H,A),并利用形变复形的上同调群来刻画模代数HA的形变,证明了HA的无穷小形变的等价类是与形变复形的2阶上同调群HH2(H,A)是一一对应的,且当HH2(H,A)=0时,模代数HA为刚性的.

We provide a 'deformation complex' CH*(H, A) associated to a given module algebra HA, and use the cohomology of CH*(H,A) to describe the infinitesimal deformation of HA. We show that there is an one-to-one correspondence between the equivalence classes of the infinitesimal deformations and HH2(H,A), and HA is rigid if the 2-cohomology of the deformaton complex HH2(H, A) = 0.