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An affine Hecke algebra of type $A_{k-1}$ is an unital, universal, associative C-algebra generated by the elements $T_1, \dots, T_{k-1}$, $X_1, \dots , X_k$, $X_1^{-1}, \dots , X_k^{-1}$ subject to eignevalue relations, $(T_i-1)(T_i-q)=0$, Laurent relations, $X_iX_j=X_jX_i$ and $X_iX_i^{-1}=X_i^{-1}X_i=1$, braid relations, $T_iT_{i+1}T_i=T_{i+1}T_iT_{i+1}$ and $T_iT_j=T_jT_i$ if $|i-j|>1$, and action relations $T_iX_iT_i=qX_{i+1}$ and $T_iX_j=X_jT_i$ if $i \neq j, j-1$. Can it be viewed as a quantum Lie algebra?

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    $\begingroup$ Hecke algebras are deformations of Weyl groups (well specifically, of their group rings), not deformations of Lie algebras. $\endgroup$
    – Sam Hopkins
    Commented Mar 24, 2021 at 23:25

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