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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
Case Study of Nonsymmetric Binary Cubic Operads 291
the relations
(((∗∗))) φ((∗∗)(∗∗)) (((∗∗))) + φ(((∗∗))) = 0,
(((∗∗))) ((∗∗)(∗∗)) φ(((∗∗))) + φ(((∗∗))) = 0
where φ is a root of the polynomial t
2
t 1.
Proof. Exercise 9.7.
Using operadic Gröbner bases, one can prove the following result on di-
mensions of components of the operads from the previous theorem.
Theorem 9.3.3.2. For the relations
(((∗∗))) = 0,
(((∗∗))) + X((∗∗)(∗∗)) = 0
and
((∗∗)(∗∗)) + X(((∗∗))) = 0,
(((∗∗))) = 0
with X F
×
, the dimension of the n-th component of the corresponding operad
is equal to
1, n = 2,
2, n = 3,
3, n = 4,
5, n = 5,
6, n 6,
and
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Publisher Resources

ISBN: 9781482248579