The tag has no wiki summary.

learn more… | top users | synonyms

0
votes
1answer
108 views

Is Khovanov's Frobenius algebra self-dual over the integers?

Khovanov's Frobenius algebra (used in the definition of Khovanov homology) is $\mathbb{Z}[X]/X^2$ with the comultiplication. $\Delta(X)=X\otimes X, \Delta(1)=1\otimes X+X\otimes 1$ and the trace ...
5
votes
5answers
387 views

Example for non equivalent rational full CFTs with same modular invariant (partition function)

I am looking for a counter example which shows, that a full rational 2D CFT (with respect to a given chiral subtheory) is not characterized by its modular invariant partition function. People tell me ...
4
votes
0answers
331 views

Partial order on partitions and symmetric group algebra

Let $n$ be a natural number. Consider a set $\Lambda_n$ of partitions of $n$ into a sum of natural numbers, like $n = \lambda_1 + \cdots +\lambda_k$ (A set of small lambdas representing a partition is ...
2
votes
1answer
272 views

Self-injective basic algebras

Do you know of any self-injective basic algebra $A$ over a field $k$ such that its enveloping algebra $A^{\mathrm{op}}\otimes_k A$ is not self-injective? The algebra $A$ cannot be finite-dimensional, ...
12
votes
3answers
469 views

Does every Frobenius algebra in a monoidal *-category give a Q-system?

Suppose that C is a fusion C*-cateogry and that A is an irreducible Frobenius algebra object in C, is there always a Frobenius algebra A' isomorphic to A such that A' is a Longo Q-system (that is the ...
10
votes
1answer
1k views

Why did people originally like Frobenius algebras?

These days, lots of people are excited by Frobenius algebras because commutative Frobenius algebras are the same thing as 2D topological quantum field theories. ...but this seems like teaching an old ...
13
votes
2answers
743 views

Cohomology rings and 2D TQFTs

There is a "folk theorem" (alternatively, a fun and easy exercise) which asserts that a 2D TQFT is the same as a commutative Frobenius algebra. Now, to every compact oriented manifold $X$ we can ...
1
vote
1answer
434 views

What is the comultiplication of a matrix frobenius algebra?

One of the easiest examples I can think of for frobenius algebras is a plain ol' matrix algebra with tr : V → k as the co-unit (or equivalently, tr(a⋅b) as the frobenius form). This is ...
3
votes
1answer
182 views

Separable and Fin. Gen. Projective but not Frobenius?

Let R be a commutative ring, and A an R-algebra (possibly non-commutative). Then A is separable if it is (fin. gen.) projective as an (A tensor_R A^op)-algebra. Suppose further that A is fin. gen. ...