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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
72 Algebraic Operads: An Algorithmic Companion
A nonsymmetric operad is a nonsymmetric collection of vector spaces
P = {P(n)}
n0
equipped with an element id P(1) and maps
i
: P(n) ⊗P(m) P(n + m 1), α β 7→ α
i
β
which satisfy the following properties for all α P(n), β P(m), γ P(r):
sequential axiom:
(α
i
β)
j
γ = α
i
(β
ji+1
γ) for i j i + m 1; (3.3)
parallel axiom:
(α
i
β)
j
γ =
(
(α
jm+1
γ)
i
β, i + m j n + m 1,
(α
j
γ)
i+r1
β, 1 j i 1;
(3.4)
unit axiom:
id
1
α = α, α
i
id = α for 1 i n. (3.5)
The following result is well known; it is featured in every textbook on
operads. Throughout this book, we will furnish some ...
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Publisher Resources

ISBN: 9781482248579