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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
166 Algebraic Operads: An Algorithmic Companion
T,T
00
2 3
1
=
2 3
1
4
.
One very useful feature of the insertion operations is that they allow us
to give an explicit description of an ideal generated by a given collection S in
the free shuffle operad which is a suitable replacement of the description “the
ideal (S) is the linear span of all elements r
1
sr
2
for all r
1
, r
2
T (X), s S
which we had in the associative case.
Proposition 5.4.2.8. Let S T
X
(X). The ideal (S) generated by S can be
described explicitly as the linear span of all insertions
T
1
,T
2
(f), where T
1
is
a shuffle tree monomial, T
2
is a divisor of T
1
, and f S(ar(T
2
)).
Proof. The ideal ...
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Publisher Resources

ISBN: 9781482248579