0
votes
1answer
108 views

Definition of the supertrace in superalgebra representations

Let us consider a matrix superalgebra $A$ with generators satisfying $[L_a,L_b]=i L_c f^c{}_{ab}.$ The generators are matrices on which supertrace is defined bu the usual trace on the bosonic part ...
1
vote
0answers
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 ...
3
votes
2answers
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 ...
8
votes
4answers
705 views

Is there a definition of analogue Weyl group for Lie super algebra?

I heard from some people working in Lie super algebra that there was no proper definition for Weyl group of Lie super algebra. I do not know Lie super algebra at all. But When I searched on Google, I ...