Given any simple Lie superalgebra g, we investigate the structure of an arbitrary simple weight g-module. We introduce two invariants of simple weight modules: the shadow and the small Weyl group. Generalizing results of Fernando and Futorny we show that any simple module is obtained by parabolic induction from a cuspidal module of a Levi subsuper-algebra. Then we classify the cuspidal Levi sub...

A Lie superalgebra is called quasi-Frobenius if it admits a closed anti-symmetric non-degenerate bilinear form. We study the notion of double extensions when form either orthosymplectic or periplectic. show that every satisfies certain conditions can be obtained as extension smaller superalgebra. classify all 4-dimensional superalgebras, and such superalgebras must solvable. [Formula: see text]...

Lie-isotopic lifting of the commutation and anticommutation relations of creation-annihilation bosonic and fermionic operators is considered. Lie-isotopic generalization of the associated supersymmetry generators and of the underlying superalgebra in considering of the Lie-isotopically lifted hamiltonian of supersymmetric quantum mechanical oscillator is defined. The generalised oscillator has ...

We study the superalgebra of the M-theory on a fully supersymmetric pp-wave. We identify the algebra as the special unitary Lie superalgebra, su(2|4 ; 2, 0) or su(2|4 ; 2, 4), and analyze its root structure. We discuss the typical and atypical representations deriving the typicality condition explicitly in terms of the energy and other four quantum numbers. We classify the BPS multiplets preser...

In this paper, we formulate a supersymmetric extension of the Euler system of equations. We compute a superalgebra of Lie symmetries of the supersymmetric system. Next, we classify the one-dimensional subalgebras of this superalgebra into 49 equivalence conjugation classes. For some of the subalgebras, the invariants have a non-standard structure. For nine selected subalgebras, we use the symme...

An orthogonal basis of weight vectors for a class of infinite-dimensional representations of the orthosymplectic Lie superalgebra osp(2m+1|2n) is introduced. These representations are particular lowest weight representations V (p), with a lowest weight of the form [−p2 , . . . ,− p 2 | p 2 , . . . , p 2 ], p being a positive integer. Explicit expressions for the transformation of the basis unde...

We introduce the concept of the Grassmann real form of an arbitrary matrix supergroup and of its Lie superalgebra. This new notion includes as special cases the ordinary real forms (considered and classified by Serganova) but it is more general. Indeed, the Grassmann real forms are characterized by certain Lie superal-gebra automorphisms of order four, while the ordinary real forms by those of ...

The quantization of the simple one-dimensional Hamiltonian H = xp is of interest for its mathematical properties rather than for its physical relevance. In fact, the Berry-Keating conjecture speculates that a proper quantization of H = xp could yield a relation with the Riemann hypothesis. Motivated by this, we study the so-called Wigner quantization of H = xp, which relates the problem to repr...