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We have the orthosymplectic $osp(n,m|2k)$. The bosonic part is $so(n,m)\times sp(2k)$. The lie algebra generators are given in eg http://cds.cern.ch/record/524737/files/0110257.pdf$where the group ... 1answer 101 views ### homomorphism of Lie superalgebras In the book Shun-Jen Cheng, Weiqiang Wang Dualities and Representations of Lie Superalgebrasm. One founds the following definition(Definition 1.3): Let$\mathfrak{g}$and$\mathfrak{g'}$be Lie ... 1answer 350 views ### 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 ... 1answer 185 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 ... 1answer 188 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 ... 1answer 435 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) ... 1answer 350 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 ... 0answers 77 views ### 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 (p.... 0answers 252 views ### 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 ... 0answers 311 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$1$-... 1answer 936 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 (... 2answers 301 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$\...
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 g}\...