# Tagged Questions

**3**

votes

**1**answer

113 views

### Linear independence in (graded) Lie algebras

I asked a mixed-up version of this question earlier.
The Lie algebras I have in mind are the homotopy Lie algebras of wedges of finitely many spheres (in dimensions greater than $1$). Thus each ...

**10**

votes

**1**answer

344 views

### What are the simple Lie superalgebras of type E?

Background
Simple finite dimensional Lie superalgebras over $\Bbb C$ have been classified. There are the Cartan type superalgebras (algebras of purely odd vector fields), two strange families P(n) ...

**1**

vote

**0**answers

298 views

### Do all finite $W$-superalgebras have 1-dimensional representations?

Premet proved the famous KW-conjecture in modular Lie algebra.
After, Premet introduced the finite $W$-algebra $U(g, e)$.
Also, Premet proposed the conjecture every algebra $U(g, e)$ admits a ...

**6**

votes

**1**answer

808 views

### I don't get a part of Bernstein's / Deligne-Morgan's proof of Poincaré-Birkhoff-Witt

Question: I am talking about the proof given on pages 50-52 of Pierre Deligne, Pavel Etingof, Daniel S. Freed, Lisa C. Jeffrey, David Kazhdan, John W. Morgan, David R. Morrison, and Edward Witten ...

**3**

votes

**2**answers

275 views

### Building Lie-like algebras from modules over semisimple Lie algebras

Here is a construction of a very broad class of "Lie-like" algebras, and I want to know more about them.
Here is the main definition: Suppose $\mathfrak{g}$ is a complex semsimple Lie algebra and ...

**10**

votes

**1**answer

300 views

### Is there much theory of superalgebras acting on manifolds by alternating polyvector fields?

Usual story: vector fields on $M$, with their Lie bracket, form a Lie algebra. We can consider "actions" of some other Lie algebra ${\mathfrak g}$ on $M$ by looking at Lie homomorphisms ${\mathfrak ...