Skip to Main Content
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
176 Algebraic Operads: An Algorithmic Companion
1 4
3
2
+
3 4
1
2
+
1 3 2 4
+
1 4 2 3
+
2 4
3
1
+
3 4
2
1
.
For the rewriting using the other divisor T
2
, we obtain:
1 2
3
4
7−→
1 3
2
4
+
2 3
1
4
7−→
1 3
4
2
+
1 3 2 4
+
1 4 2 3
+
2 3
4
1
7−→
1 4
3
2
+
3 4
1
2
+
1 3 2 4
+
1 4 2 3
+
2 4
3
1
+
3 4
2
1
.
(In each of these cases, each arrow represents several rewritings of all non-
reduced monomials in one go.) We see that the results are the same, so the
corresponding S-polynomial can be reduced to zero, and the defining relation
of the operad Lie
f
is the reduced Gröbner basis. A similar computation shows
that in this case for each of the monomials in the defining relation, and any
Symmetric Operads and Shuffle Operads
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Start your free trial

You might also like

Reinventing the Organization for GenAI and LLMs

Reinventing the Organization for GenAI and LLMs

Ethan Mollick
Algebraic and Stochastic Coding Theory

Algebraic and Stochastic Coding Theory

Dave K. Kythe, Prem K. Kythe

Publisher Resources

ISBN: 9781482248579