Related papers: On Casimir's Ghost
We present a construction of curved analogues of the nonstandard operators on Grassmannians parallel to the construction of the Paneitz operator via the curved Casimir operator, but technically more demanding. In particular, the…
A new supersymmetrization of the so-called AdS-Lorentz algebra is presented. It involves two fermionic generators and is obtained by performing an abelian semigroup expansion of the superalgebra osp(4|1). The peculiar properties of the…
The N-extended Supersymmetric Quantum Mechanics is deformed via an abelian twist which preserves the super-Hopf algebra structure of its Universal Enveloping Superalgebra. Two constructions are possible. For even N one can identify the 1D…
We study representations of the simple Lie antialgebra $asl_2$ introduced by Ovsienko. We show that representations of $asl_2$ are closely related to the famous ghost Casimir element of the universal enveloping algebra $osp(1|2)$. We prove…
We describe a general conjecture on how one may derive from the generic bosonic case all structural properties of multivariate diagonal coinvariant modules in $k$ sets of $n$ commuting variables (bosons), and $j$ sets of $n$ anticommuting…
An extension of the Poincar\'e group with half-integer spin generators is explicitly constructed. We start discussing the case of three spacetime dimensions, and as an application, it is shown that hypergravity can be formulated so as to…
A counterpart of the modular double for quantum superalgebra $\cU_q(\osp(1|2))$ is constructed by means of supersymmetric quantum mechanics. We also construct the $R$-matrix operator acting in the corresponding representations, which is…
We study some of the algebraic properties of the non-relativistic monopole. We find that we can construct theories that possess an exotic conserved fermionic charge that squares to the Casimir of the rotation group, yet do not possess an…
Supersymmetric bosonic backgrounds governed by first-order BPS equations, can be realised in a much broader setting by relaxing the requirement of closure of the superalgebra beyond the level of quadratic fermion terms. The resulting…
A linear degenerate odd Poisson bracket (antibracket) realized solely on Grassmann variables is presented. It is revealed that this bracket has at once three nilpotent $\Delta$-like differential operators of the first, the second and the…
We give a new interpretation for the super loop space that has been used to formulate supersymmetry. The fermionic coordinates in the super loop space are identified as the odd generators of the Weil algebra. Their bosonic superpartners are…
We show that a simple change of the classical boson-fermion coupling constant, $2\alpha \to 2\alpha n $, $n\in \N$, in the superconformal mechanics model gives rise to a radical change of a symmetry: the modified classical and quantum…
A complete choice of generators of the center of the enveloping algebras of real quasi-simple Lie algebras of orthogonal type, for arbitrary dimension, is obtained in a unified setting. The results simultaneously include the well known…
We consider the simplest nontrivial supersymmetric quantum mechanical system involving higher derivatives. We unravel the existence of additional bosonic and fermionic integrals of motion forming a nontrivial algebra. This allows one to…
Based on the superconformal algebra we construct a dual operator that introduces a grading among bosonic generators independent of the boson/fermion grading of the superalgebra. This dual operator allows us to construct an action that is…
A linear odd Poisson bracket (antibracket) realized solely in terms of Grassmann variables is suggested. It is revealed that the bracket, which corresponds to a semi-simple Lie group, has at once three Grassmann-odd nilpotent $\Delta$-like…
Using the notion of a gauge connection on a flat superspace, we construct a general class of noncommutative ($D=2,$ $\mathcal{N}=1$) supertranslation algebras generalizing the ordinary algebra by inclusion of some new bosonic and fermionic…
We propose a new generalization of the standard (anti-)commutation relations for creation and annihilation operators of bosons and fermions. These relations preserve the usual symmetry properties of bosons and fermions. Only the standard…
A tensor extension of the Poincar\'e algebra is proposed for the arbitrary dimensions. Casimir operators of the extension are constructed. A possible supersymmetric generalization of this extension is also found in the dimensions $D=2,3,4$.
We consider supersymmetric extensions of a recently proposed partonic description of a bosonic p-brane which reformulates the Nambu-Goto action as an interacting multi-particle action with Filippov-Lie algebra gauge symmetry. We construct a…