Multiparticle extension of the higher-spin algebra

Understand

Multiparticle extension of a higher-spin algebra $l$ is introduced as the Lie superalgebra associated with the universal enveloping algebra $U(l)$.

• While conventional higher-spin symmetry does not mix $n$-particle states with different $n$, multiparticle symmetries do so.
• Quotients of multiparticle algebras are considered, that act on the space of $n$-particle states with $0\leq n\leq k$ analogous to the space of first $k$ Regge trajectories of String Theory.
• Original higher-spin algebra is reproduced at $k=1$.