相关论文: On contractions of classical basic superalgebras

We define a class of orthosymplectic superalgebras $osp(m;j|2n;\omega)$ which may be obtained from $osp(m|2n)$ by contractions and analytic continuations in a similar way as the orthogonal and the symplectic Cayley-Klein algebras are…

We study here the generalized Weimar-Woods contractions of the superalgebra $osp(1|32) \oplus osp(1|32)$ in order to obtain a suitable algebra that could describe the gauge group of $D=11$ supergravity. The contracted superalgebras are…

We develop a generic reprersentation-independent contraction procedure for obtaining, for instance, $R_{\sf h}$ and $L$ operators of arbitrary dimensions for the quantized ${\cal U}_{\sf h}(osp(2|1))$ algebra corresponding to the classical…

Triangular deformation of the orthosymplectic Lie superalgebra osp(1|4) is defined by chains of twists. Corresponding classical r-matrix is obtained by a contraction procedure from the trigonometric r-matrix. The carrier space of the…

We explicitly compute the first and second cohomology groups of the classical Lie superalgebras $sl_{m|n}$ and $osp_{2|2n}$ with coefficients in the finite dimensional irreducible modules and the Kac modules. We also show that the second…

We study $\Bbb Z_2^{\otimes N}$ graded contractions of the real compact simple Lie algebra $so(N+1)$, and we identify within them the Cayley-Klein algebras as a naturally distinguished subset.

Linear operators preserving the direct sum of polynomial rings P(m)\oplus P(n) are constructed. In the case |m-n|=1 they correspond to atypical representations of the superalgebra osp(2,2). For |m-n|=2 the generic, finite dimensional…

After reviewing the three well-known methods to obtain Lie algebras and superalgebras from given ones, namely, contractions, deformations and extensions, we describe a fourth method recently introduced, the expansion of Lie (super)algebras.…

Contractions (and graded contractions) of Lie algebra, Lie bialgebra and Hopf algebra are discussed. It is noticed the fundamental role of E.In{\"o}n{\"u} and E.P.Wigner idea of degenerate transformations. A constructive algorithm for…

We introduce the orthosymplectic superalgebra osp(m|2n) as the algebra of Killing vector fields on Riemannian superspace R^{m|2n} which stabilize the origin. The Laplace operator and norm squared on R^{m|2n}, which generate sl(2), are…

We note that large classes of contractions of algebras that arise in physics can be understood purely algebraically, via identifying appropriate $\mathbb{Z}_m$-gradings (and their generalizations) on the parent algebra. This includes…

We study and classify kinematical algebras which appear in the framework of Lie superalgebras or Lie algebras of order three. All these algebras are related through generalised Inon\"u-Wigner contractions from either the orthosymplectic…

We will derive both quaternion and octonion algebras as the Clebsch-Gordan algebras based upon the su(2) Lie algebra by considering angular momentum spaces of spin one and three. If we consider both spin 1 and 1/2 states, then the same…

Generalizations of the (rank 1) Bannai-Ito algebra are obtained from a refinement of the grade involution of the Lie super algebra $\mathfrak{osp}(1,2)$. A hyperoctahedral extension is derived by using a realization of $\mathfrak{osp}(1,2)$…

The quantum-to-classical transition is considered from the point of view of contractions of associative algebras. Various methods and ideas to deal with contractions of associative algebras are discussed that account for a large family of…

For the orthogonal Lie algebra O(2n+1), in addition to the conventional set of orthogonal polynomials, another set is produced with the help of the Lie superalgebra OSP(1|2n). Difficulties related with expression of Dyson's constant for the…

It turns out that harmonic analysis on the superspace R^{m|2n} is quite parallel to the classical theory on the Euclidean space R^{m} unless the superdimension M:=m-2n is even and non-positive. The underlying symmetry is given by the…

We introduce the umbral calculus formalism for hypercomplex variables starting from the fact that the algebra of multivariate polynomials $\BR[\underline{x}]$ shall be described in terms of the generators of the Weyl-Heisenberg algebra. The…

We study Yang-Baxter equations with orthosymplectic supersymmetry. We extend a new approach of the construction of the spinor and metaplectic $\hat{\cal R}$-operators with orthogonal and symplectic symmetries to the supersymmetric case of…

We determine the skew fields of fractions of the enveloping algebra of the Lie superalgebra osp(1, 2) and of some significant subsu-peralgebras of the Lie superalgebra osp(1, 4). We compare the kinds of skew fields arising from this "super"…