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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
Nonsymmetric Operads 97
an overlap. We call this overlap essential if lm(g
1
) and lm(g
2
) are the only
two divisors from lm(G) of the tree monomial obtained by merging these
monomials along their overlap.
Proposition 3.5.3.2 (Triangle lemma for nonsymmetric operads). Let G be
a self-reduced subset of T (X), and let g
1
, g
2
G be two elements for which
lm(g
1
) and lm(g
2
) have an overlap. Suppose that this overlap is not essential,
so that there exists g
3
G for which lm(g
3
) is another divisor of the tree
monomial T obtained by merging lm(g
1
) and lm(g
2
) along their overlap. Then:
The divisors lm(g
1
) and lm(g
3
) of T have an overlap, and the divisors
lm(g
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Publisher Resources

ISBN: 9781482248579