28 research outputs found
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
Assessment of skeletal maturity: a new classification scheme using distal radius and ulna radiographs
Concurrent Session 6A - Innovative & Diagnostic Methods: paper no. 97SUMMARY: Our study describes a new classification scheme to assess skeletal maturity by utilizing the distal radius and ulna radiographs. This classification demonstrates a relationship with adolescent growth spurt and cessation of growth. Introduction: The progression of the curve in adolescent idiopathic scoliosis has always been associated with pubertal growth spurt. The commonly used clinical or radiological methods are still deficient in predicting this growth peak among adolescents and bone age is too complicated to apply. To address these concerns, we ...postprin
On sl(2)-equivariant quantizations
By computing certain cohomology of Vect(M) of smooth vector fields we prove
that on 1-dimensional manifolds M there is no quantization map intertwining the
action of non-projective embeddings of the Lie algebra sl(2) into the Lie
algebra Vect(M). Contrariwise, for projective embeddings sl(2)-equivariant
quantization exists.Comment: 09 pages, LaTeX2e, no figures; to appear in Journal of Nonlinear
Mathematical Physic
Classification of Finite Dimensional Modular Lie Superalgebras with Indecomposable Cartan Matrix
Finite dimensional modular Lie superalgebras over algebraically closed fields with indecomposable Cartan matrices are classified under some technical, most probably inessential, hypotheses. If the Cartan matrix is invertible, the corresponding Lie superalgebra is simple otherwise the quotient of the derived Lie superalgebra modulo center is simple (if its rank is greater than 1). Eleven new exceptional simple modular Lie superalgebras are discovered. Several features of classic notions, or notions themselves, are clarified or introduced, e.g., Cartan matrix, several versions of restrictedness in characteristic 2, Dynkin diagram, Chevalley generators, and even the notion of Lie superalgebra if the characteristic is equal to 2. Interesting phenomena in characteristic 2: (1) all simple Lie superalgebras with Cartan matrix are obtained from simple Lie algebras with Cartan matrix by declaring several (any) of its Chevalley generators odd; (2) there exist simple Lie superalgebras whose even parts are solvable. The Lie superalgebras of fixed points of automorphisms corresponding to the symmetries of Dynkin diagrams are also listed and their simple subquotients described
Cohomology of the Lie Superalgebra of Contact Vector Fields on and Deformations of the Superspace of Symbols
Following Feigin and Fuchs, we compute the first cohomology of the Lie
superalgebra of contact vector fields on the (1,1)-dimensional
real superspace with coefficients in the superspace of linear differential
operators acting on the superspaces of weighted densities. We also compute the
same, but -relative, cohomology. We explicitly give
1-cocycles spanning these cohomology. We classify generic formal
-trivial deformations of the -module
structure on the superspaces of symbols of differential operators. We prove
that any generic formal -trivial deformation of this
-module is equivalent to a polynomial one of degree .
This work is the simplest superization of a result by Bouarroudj [On
(2)-relative cohomology of the Lie algebra of vector fields and
differential operators, J. Nonlinear Math. Phys., no.1, (2007), 112--127].
Further superizations correspond to -relative cohomology
of the Lie superalgebras of contact vector fields on -dimensional
superspace
Real forms of the complex twisted N=2 supersymmetric Toda chain hierarchy in real N=1 and twisted N=2 superspaces
Three nonequivalent real forms of the complex twisted N=2 supersymmetric Toda
chain hierarchy (solv-int/9907021) in real N=1 superspace are presented. It is
demonstrated that they possess a global twisted N=2 supersymmetry. We discuss a
new superfield basis in which the supersymmetry transformations are local.
Furthermore, a representation of this hierarchy is given in terms of two
twisted chiral N=2 superfields. The relations to the s-Toda hierarchy by H.
Aratyn, E. Nissimov and S. Pacheva (solv-int/9801021) as well as to the
modified and derivative NLS hierarchies are established
The classification of almost affine (hyperbolic) Lie superalgebras
We say that an indecomposable Cartan matrix A with entries in the ground
field of characteristic 0 is almost affine if the Lie sub(super)algebra
determined by it is not finite dimensional or affine but the Lie (super)algebra
determined by any submatrix of A, obtained by striking out any row and any
column intersecting on the main diagonal, is the sum of finite dimensional or
affine Lie (super)algebras. A Lie (super)algebra with Cartan matrix is said to
be almost affine if it is not finite dimensional or affine, and all of its
Cartan matrices are almost affine.
We list all almost affine Lie superalgebras over complex numbers correcting
two earlier claims of classification and make available the list of almost
affine Lie algebras obtained by Li Wang Lai.Comment: 92 page
The ternary invariant differential operators acting on the spaces of weighted densities
Over n-dimensional manifolds, I classify ternary differential operators
acting on the spaces of weighted densities and invariant with respect to the
Lie algebra of vector fields. For n=1, some of these operators can be expressed
in terms of the de Rham exterior differential, the Poisson bracket, the Grozman
operator and the Feigin-Fuchs anti-symmetric operators; four of the operators
are new, up to dualizations and permutations. For n>1, I list multidimensional
conformal tranvectors, i.e.,operators acting on the spaces of weighted
densities and invariant with respect to o(p+1,q+1), where p+q=n. Except for the
scalar operator, these conformally invariant operators are not invariant with
respect to the whole Lie algebra of vector fields.Comment: 13 pages, no figures, to appear in Theor. Math. Phy
Regional and experiential differences in surgeon preference for the treatment of cervical facet injuries: a case study survey with the AO Spine Cervical Classification Validation Group
Purpose: The management of cervical facet dislocation injuries remains controversial. The main purpose of this investigation was to identify whether a surgeon’s geographic location or years in practice influences their preferred management of traumatic cervical facet dislocation injuries. Methods: A survey was sent to 272 AO Spine members across all geographic regions and with a variety of practice experience. The survey included clinical case scenarios of cervical facet dislocation injuries and asked responders to select preferences among various diagnostic and management options. Results: A total of 189 complete responses were received. Over 50% of responding surgeons in each region elected to initiate management of cervical facet dislocation injuries with an MRI, with 6 case exceptions. Overall, there was considerable agreement between American and European responders regarding management of these injuries, with only 3 cases exhibiting a significant difference. Additionally, results also exhibited considerable management agreement between those with ≤ 10 and > 10 years of practice experience, with only 2 case exceptions noted. Conclusion: More than half of responders, regardless of geographical location or practice experience, identified MRI as a screening imaging modality when managing cervical facet dislocation injuries, regardless of the status of the spinal cord and prior to any additional intervention. Additionally, a majority of surgeons would elect an anterior approach for the surgical management of these injuries. The study found overall agreement in management preferences of cervical facet dislocation injuries around the globe