314 research outputs found
General form of the deformation of Poisson superbracket on (2,2)-dimensional superspace
Continuous formal deformations of the Poisson superbracket defined on
compactly supported smooth functions on n-dimensional space taking values in a
Grassmann algebra with m generating elements are described up to an equivalence
transformation for the case n=m=2. It is shown that in this case the Poisson
superalgebra has an additional deformation comparing with other superdimensions
(n,m).Comment: LaTex, 13 page
Minkowski superspaces and superstrings as almost real-complex supermanifolds
In 1996/7, J. Bernstein observed that smooth or analytic supermanifolds that
mathematicians study are real or (almost) complex ones, while Minkowski
superspaces are completely different objects. They are what we call almost
real-complex supermanifolds, i.e., real supermanifolds with a non-integrable
distribution, the collection of subspaces of the tangent space, and in every
subspace a complex structure is given.
An almost complex structure on a real supermanifold can be given by an even
or odd operator; it is complex (without "always") if the suitable superization
of the Nijenhuis tensor vanishes. On almost real-complex supermanifolds, we
define the circumcised analog of the Nijenhuis tensor. We compute it for the
Minkowski superspaces and superstrings. The space of values of the circumcised
Nijenhuis tensor splits into (indecomposable, generally) components whose
irreducible constituents are similar to those of Riemann or Penrose tensors.
The Nijenhuis tensor vanishes identically only on superstrings of
superdimension 1|1 and, besides, the superstring is endowed with a contact
structure. We also prove that all real forms of complex Grassmann algebras are
isomorphic although singled out by manifestly different anti-involutions.Comment: Exposition of the same results as in v.1 is more lucid. Reference to
related recent work by Witten is adde
Cohomology of Lie superalgebras and of their generalizations
The cohomology groups of Lie superalgebras and, more generally, of color Lie
algebras, are introduced and investigated. The main emphasis is on the case
where the module of coefficients is non-trivial. Two general propositions are
proved, which help to calculate the cohomology groups. Several examples are
included to show the peculiarities of the super case. For L = sl(1|2), the
cohomology groups H^1(L,V) and H^2(L,V), with V a finite-dimensional simple
graded L-module, are determined, and the result is used to show that
H^2(L,U(L)) (with U(L) the enveloping algebra of L) is trivial. This implies
that the superalgebra U(L) does not admit of any non-trivial formal
deformations (in the sense of Gerstenhaber). Garland's theory of universal
central extensions of Lie algebras is generalized to the case of color Lie
algebras.Comment: 50 pages, Latex, no figures. In the revised version the proof of
Lemma 5.1 is greatly simplified, some references are added, and a pertinent
result on sl(m|1) is announced. To appear in the Journal of Mathematical
Physic
Superconformal Primary Fields on a Graded Riemann Sphere
Primary superfields for a two dimensional Euclidean superconformal field
theory are constructed as sections of a sheaf over a graded Riemann sphere. The
construction is then applied to the N=3 Neveu-Schwarz case. Various quantities
in the N=3 theory are calculated and discussed, such as formal elements of the
super-Mobius group, and the two-point function.Comment: LaTeX2e, 23 pages; fixed typos, sorted references, modified
definition of primary superfield on page
Cohomologies of the Poisson superalgebra
Cohomology spaces of the Poisson superalgebra realized on smooth
Grassmann-valued functions with compact support on ($C^{2n}) are
investigated under suitable continuity restrictions on cochains. The first and
second cohomology spaces in the trivial representation and the zeroth and first
cohomology spaces in the adjoint representation of the Poisson superalgebra are
found for the case of a constant nondegenerate Poisson superbracket for
arbitrary n>0. The third cohomology space in the trivial representation and the
second cohomology space in the adjoint representation of this superalgebra are
found for arbitrary n>1.Comment: Comments: 40 pages, the text to appear in Theor. Math. Phys.
supplemented by computation of the 3-rd trivial cohomolog
Irreducible holonomy algebras of Riemannian supermanifolds
Possible irreducible holonomy algebras \g\subset\osp(p,q|2m) of Riemannian
supermanifolds under the assumption that \g is a direct sum of simple Lie
superalgebras of classical type and possibly of a one-dimensional center are
classified. This generalizes the classical result of Marcel Berger about the
classification of irreducible holonomy algebras of pseudo-Riemannian manifolds.Comment: 27 pages, the final versio
On Alternative Supermatrix Reduction
We consider a nonstandard odd reduction of supermatrices (as compared with
the standard even one) which arises in connection with possible extension of
manifold structure group reductions. The study was initiated by consideration
of the generalized noninvertible superconformal-like transformations. The
features of even- and odd-reduced supermatrices are investigated on a par. They
can be unified into some kind of "sandwich" semigroups. Also we define a
special module over even- and odd-reduced supermatrix sets, and the generalized
Cayley-Hamilton theorem is proved for them. It is shown that the odd-reduced
supermatrices represent semigroup bands and Rees matrix semigroups over a unit
group.Comment: 22 pages, Standard LaTeX with AmS font
Orthogonal polynomials of discrete variable and Lie algebras of complex size matrices
We give a uniform interpretation of the classical continuous Chebyshev's and
Hahn's orthogonal polynomials of discrete variable in terms of Feigin's Lie
algebra gl(N), where N is any complex number. One can similarly interpret
Chebyshev's and Hahn's q-polynomials and introduce orthogonal polynomials
corresponding to Lie superlagebras.
We also describe the real forms of gl(N), quasi-finite modules over gl(N),
and conditions for unitarity of the quasi-finite modules. Analogs of tensors
over gl(N) are also introduced.Comment: 25 pages, LaTe
Minimal deformations of the commutative algebra and the linear group GL(n)
We consider the relations of generalized commutativity in the algebra of
formal series , which conserve a tensor -grading and
depend on parameters . We choose the -preserving version of
differential calculus on . A new construction of the symmetrized tensor
product for -type algebras and the corresponding definition of minimally
deformed linear group and Lie algebra are proposed. We
study the connection of and with the special matrix
algebra \mbox{Mat} (n,Q) containing matrices with noncommutative elements.
A definition of the deformed determinant in the algebra \mbox{Mat} (n,Q) is
given. The exponential parametrization in the algebra \mbox{Mat} (n,Q) is
considered on the basis of Campbell-Hausdorf formula.Comment: 14 page
Attitudes of Germans towards distributive issues in the German health system
Social health care systems are inevitably confronted with the scarcity of resources and the resulting distributional challenges. Since prioritization implies distributional effects, decisions on respective rules should take citizens’ preferences into account. Thus, knowledge about citizens’ attitudes and preferences regarding different distributional issues implied by the type of financing health care is necessary to judge the public acceptance of a health system. In this study we concentrate on two distributive issues in the German health system: First, we analyse the acceptance of prioritizing decisions concerning the treatment of certain patient groups, in this case patients who all need a heart operation. Here we focus on the fact that a patient is strong smoker or a non-smoker, the criteria of age or the fact that a patient has or does not have young children. Second, we investigate Germans’ opinions towards income dependent health services. The results reveal strong effects of individuals’ attitudes regarding general aspects of the health system on priorities, e.g. that individuals behaving health demanding should not be preferred. In addition, experiences of limited access to health services are found to have a strong influence on citizens’ attitudes, too. Finally, decisions about different prioritization criteria are found to be not independent.
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