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homomorphism of Lie superalgebras

In the book Shun-Jen Cheng, Weiqiang Wang Dualities and Representations of Lie Superalgebrasm. One founds the following definition(Definition 1.3): Let $\mathfrak{g}$ and $\mathfrak{g'}$ be Lie ...
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Kauffman's state model for the Alexander polynomial, via representation theory

I've been reading Oleg Viro's paper on "quantum relatives of the Alexander polynomial" (arXiv:math/0204290), which, among other more general things, derives state-sum formulas for the Alexander ...
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117 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 ...
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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 ...
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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) ...
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322 views

Lie superalgebra in two dimensions

The standard formulation of two dimensional $N=(2,2)$ and $N=(0,2)$ supersymmetry algebras in physics is an explicit one; I am not aware of the underlying abstract Lie superalgebras. Does anyone know ...
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Finite dimensional consistently graded Lie superalgebras of depth greater than 2

Victor Kac, in the paper "Classification of infinite-dimensional simple linearly compact Lie superalgebras", http://www.mat.univie.ac.at/~esiprpr/esi605.pdf writes at the beginning of section 5 ...
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Is the SUSY Algebra isomorphic for all Kähler Manifolds?

For a Kähler manifold, the graded algebra generated by $\partial,\overline{\partial},\partial^*,\overline{\partial}^\ast$, the Lefschetz operator, and the dual Lefschetz operator, is called the ...
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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 ...
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810 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 ...
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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 ...
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301 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 ...
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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 ...