To phrase the question in a concrete way, I read in a paper:
The super Poincare subalgebra of osp(6,2|4) has bosonic part $so(5,1) \oplus usp(4) \simeq so(5,1) \oplus so(5)$.
It's hard to unpack this sentence without knowing the objects:
- Can the orthosymplectic group osp(6,2|4) be defined as a group of matrices acting on a super-vector space?
- Can someone explain this decomposition into its bosonic and fermionic parts?
- What is the (super) Poincare sub-algebra? Why is usp(4) the same is so(5)?
For a math-physics dictionary: "super" means "Z2-graded" while bosonic means "0-grade" and fermionic means "1-grade".