Solutions to the Yang–Baxter equation are often constrained by requiring the R matrix to be invariant under the action of a Lie group G . For example, in the case G = G L ( V ) and R ( u , u ′ ) ∈ ∈ End ( V ⊗ ⊗ V ) , the only G -invariant maps in End ( V ⊗ ⊗ V ) are the identity I and the permutation map P . The general form of the R -matrix is then R ( u , u ′ ) = A ( u , u ′ ) I + B ( u , u ′ ) P for scalar functions A , B .