The super-algebra tag has no wiki summary.

**3**

votes

**0**answers

65 views

### How well is the classification of low-dimensional semisimple Hopf superalgebras (or braided Hopf algebras) understood?

As far as I know, low-dimensional semisimple Hopf algebras are classified (along with non-semisimple ones) up to dimension 60, with the first example of a semisimple Hopf algebra not coming from a ...

**1**

vote

**0**answers

86 views

### Supertrace on Weyl algebra

Consider Weyl algebra, i.e. the algebra of $x^i$ and $p_i=\frac{\partial}{\partial x^i}$,
its elements are differential operators $F(x,p)$. Weyl algebra is $\mathbb{Z}_2$ graded, hence one ask if ...

**4**

votes

**0**answers

79 views

### Tensor categories with integer rank

I wonder the state of the following conjecture in "Deformation theory, Kontsevich, Soibelman":
Conjecture 3.3.5. Rigid [abelian symmetric] tensor categories [over an algebraically closed field $k$] ...

**3**

votes

**1**answer

61 views

### Does every equivalence class in a Brauer-Wall group have a (graded) division algebra?

It is known that each equivalence class in a Brauer group has a division algebra (or, in other words, every central simple algebra is isomorphic to $\mathrm{Mat}(D)$ for some division algebra $D$). Is ...

**0**

votes

**0**answers

45 views

### Grassmann algebra morphism with universal property

I'm pretty sure that the following doesn't work, but nevertheless i wanted to ask, maybe this is a kind of well-known construction i've never heard of:
Let $\Lambda(\mathbb{R}^n)$ be a finite ...

**3**

votes

**1**answer

247 views

### A good reference for learning about super-differentiation & super-integration?

I've looked at a couple of books for basic information for super-differentiation & super-integration - Rogers Supermanifolds, and Khrennikovs Superanalysis.
Unfortunately both books lack a clear ...

**4**

votes

**0**answers

120 views

### FRT construction in the case of super algebras

I'm looking on papers which are talking about the super quantum algebra osp(2|1). I want to understand how one applies the FRT construction in the case of osp(2|1).
Of course there is a super ...

**3**

votes

**0**answers

155 views

### Super group GL(m,m) and Koszul (deRham) complex. (Is there brigde from super-math to usual-math ?)

Consider vector space with coordinates x1, ... xn. Consider polynomial deRham complex (also known as Koszul complex) which is generated by xi and dx_i. As an algebra it is just $C[x_i]\otimes \Lambda ...

**5**

votes

**2**answers

582 views

### How can I write down a point in the Berezinian of a super vector space?

A vector space $V$ of dimension $n$ has an associated determinant line $Det(V)$.
An element of $Det(V)$ is represented as a (formal limear combination) of expresstions of the form
$v_1 \wedge ...

**3**

votes

**1**answer

910 views

### Witten Index, letter partition function and superconformal representations.

Except in a few papers I have seen so little written about this that I am not sure I can even frame this question properly.
I would like to know of expository references and explanations on the ...

**5**

votes

**3**answers

497 views

### Derivations of C(X)? or Why Must Supermanifolds be Smooth?

What are the derivations of the algebra of continuous functions on a topological manifold?
A supermanifold is a locally ringed space (X,O) whose underlying space is a smooth manifold X, and whose ...

**6**

votes

**1**answer

439 views

### Does some version of U_q(gl(1|1)) have a basis like Lusztig's basis for \dot{U(sl_2)}?

There's a non-unital algebra $\dot{U}$ formed from $U_q (sl_2)$ by including a system of mutually orthogonal idempotents $1_n$, indexed by the weight lattice. You can think of this as a category with ...