2
votes
1answer
170 views

PROPs representations, free module analog

Ordinary operad with one ouput can be obviously regarded as free module on itself. Is there are analogous construction for operad with many outputs (PROP)? This must be difficult question, but what is ...
8
votes
1answer
211 views

Generating the graded S_n-module associated to an operad

Suppose I have a symmetric operad $\mathcal{P}$ defined over $\text{Vect}_{\mathbb{K}}$ with generators and relations in degrees at most $l$. Now suppose I already know $\mathcal{P}(k)$ as an ...
0
votes
0answers
333 views

[]-infinity algebra and Projective representation

This is a very vague question. We know that some algebra structures can be viewed as modules of some fantastic stuff, call T. Such examples include: Abelian groups are $\mathbb{Z}$-modules, chain ...
5
votes
1answer
436 views

Where does the definition of “Tower of Algebras” come from?

A tower of algebras is a sequence of algebras $$A_0 \hookrightarrow A_1 \hookrightarrow \cdots \hookrightarrow A_n \hookrightarrow \cdots$$ with embeddings $A_n \otimes A_m \hookrightarrow A_{n+m}$ ...
12
votes
2answers
508 views

GL(V)-representation theory for a Lie bracket kernel

Let $V$ be a vector space over a field of characteristic $0$, and let $L_k(V)$ be the degree $k$ part of the free Lie algebra over $V$. There is an exact sequence $$0\to D_n(V)\to L_1(V)\otimes ...