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Algebraic Operads
book

Algebraic Operads

by Murray R. Bremner, Vladimir Dotsenko
April 2016
Intermediate to advanced content levelIntermediate to advanced
383 pages
11h 46m
English
Chapman and Hall/CRC
Content preview from Algebraic Operads
156 Algebraic Operads: An Algorithmic Companion
Corollary 5.3.3.3. Let M be a symmetric collection. Then we have an iso-
morphism of shuffle operads
T
X
(M
f
)
=
(T
Σ
(M))
f
.
Moreover, if I T
Σ
(M) is an ideal, then, under the identification that we
made, I
f
is an ideal of T
X
(M
f
), and
T
X
(M
f
)/I
f
=
(T
Σ
(M)/I)
f
.
Proof. All the notions in question, that is free symmetric operads, free shuffle
operads, and ideals in those operads, are defined using composition products,
so Proposition 5.3.3.1 applies.
Example 5.3.3.4. Let us consider the free shuffle operad T
X
(X) from Ex-
ample 5.3.1.3. Note that it is isomorphic to T
Σ
(L)
f
, where L is the symmetric
collection from Example 5.2.2.4: ...
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Publisher Resources

ISBN: 9781482248579