
118 Algebraic Operads: An Algorithmic Companion
4.2.2 Free twisted associative algebras
Similar to the case of associative algebras, a twisted associative algebra
can be presented via generators and relations, that is, as a quotient of the free
twisted associative algebra T
Σ
(M), which we will now describe, by some ideal.
Unlike the cases of the free associative algebra and the free nonsymmetric op-
erad, we will not discuss free twisted associative algebras in full detail, since we
will see that they are not fully suitable for defining Gröbner bases and proving
an appropriate diamond lemma (which leads to a suitable replacement, free
shuffle algebras,