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
138 Algebraic Operads: An Algorithmic Companion
Definition 4.6.3.2 (Commutative shuffle algebra). A shuffle algebra A for
which
µ
I
1
,I
2
(a
1
, a
2
) = µ
I
2
,I
1
(a
2
, a
1
)
whenever {1, . . . , n} = I
1
t I
2
, a
1
A(|I
1
|), a
2
A(|I
2
|), is said to be com-
mutative.
The most important example of a twisted commutative algebra is the ten-
sor algebra of a vector space.
Proposition 4.6.3.3. The tensor algebra T (V ) with its shuffle algebra struc-
ture is commutative. In fact, it is free as a commutative shuffle algebra.
Proof. The first statement is trivially true; it is essentially explained in the
introduction to this chapter. The second statement is left as an exercise for
the
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