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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
202 Algebraic Operads: An Algorithmic Companion
by the signs that come from compositions in S
1
. Therefore, if we denote
the generator of As
q
and the generator of As
!
q
by the same symbol , the
pairing in question satisfies
*
,
+
=
*
,
+
.
In addition, we of course have
*
,
+
= 0 =
*
,
+
.
The usual convention is to put
*
,
+
= 1,
*
,
+
= 1.
In this case, the dual of the defining relation
q = 0
of As
q
is the relation
q = 0.
In other words, As
!
q
=
As
q
1
(for q 6= 0).
Example 6.3.2.2. Consider the shuffle operad Lie
f
which, as we know from
Example 5.3.4.2, is the operad with just one defining relation
1 2
3
2 3
1
1 3
2
= 0.
In the shuffle case, in addition to the property highlighted in Example ...
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Publisher Resources

ISBN: 9781482248579