Eric Forgy algebra of projections

Skip the Navigation Links | Home Page | All Pages |

Definition

Given a set SS, the algebra of projections on SS is the commutative algebra 𝒜\mathcal{A} spanned by the projections

{π s:S→S|s∈S}\{\pi_s:S\to S|s\in S\}

satisfying

∑ s∈Sπ s=1\sum_{s\in S} \pi_s = 1

whose bilinear product m:𝒜⊗𝒜→𝒜m:\mathcal{A}\otimes\mathcal{A}\to\mathcal{A} is given by

m(π s⊗π s′)=δ s,s′π s.m(\pi_s\otimes\pi_{s'}) = \delta_{s,s'} \pi_s.

Note to Self

See Section 3.1 of

category: maths

Revised on April 10, 2011 at 16:18:22 by Eric Forgy