Basic geometry of G-supermanifolds

Bartocci, Claudio; Bruzzo, Ugo; Hernández-Ruipérez, Daniel

doi:10.1007/978-94-011-3504-7_4

Cited by 10 publications

(42 citation statements)

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“…The numbering used is the same as for the helicene, with the addition of the two hydrogens (15 and 16) borne by the carbon atoms were the closure occurs. [37] [15] R f = 0.20 (AcOEt/hexane, 5:1). Yield: 78 %; m. p. 216-219°C.…”

Section: -Quinolinecarbaldehyde and 3-isoquinolinecarbaldehydementioning

confidence: 99%

Synthesis and Characterization of Some Aza[5]helicenes

et al. 2005

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A systematic study on the synthesis and properties of aza- [5]helicenes bearing one or two nitrogen atoms in selected ring positions is reported for the first time. This photochemical approach can be conveniently applied to the preparation of either mono- or diaza[5]helicenes. The aza[5]helicenes were characterized by NMR spectroscopy, X-ray crystallography, emission spectroscopy, and luminescence lifetime. The extremely long triplet lifetime observed (in the range of seconds) makes these molecules promising candidates for practical applications in photo- and optoelectronics

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Section: -Quinolinecarbaldehyde and 3-isoquinolinecarbaldehydementioning

confidence: 99%

Synthesis and Characterization of Some Aza[5]helicenes

et al. 2005

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“…is a graded manifold [2]. Consequently the map β X from the Z 2 -graded C-algebra H ∞ (X, C L ) to the (trivially Z 2 -graded) C-algebra C ∞ (X, C) of smooth complex-valued functions on X, defined by…”

Section: The (2|2)-dimensional Superspherementioning

confidence: 99%

The fuzzy supersphere

Grosse

Reiter

1998

Journal of Geometry and Physics

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We introduce the fuzzy supersphere as sequence of finite-dimensional, noncommutative Z 2 -graded algebras tending in a suitable limit to a dense subalgebra of the Z 2 -graded algebra of H ∞ -functions on the (2|2)-dimensional supersphere. Noncommutative analogues of the body map (to the (fuzzy) sphere) and the super-deRham complex are introduced. In particular we reproduce the equality of the super-deRham cohomology of the supersphere and the ordinary deRham cohomology of its body on the "fuzzy level". osp(1|2) [4,42,43], which correspond, when restricted to the even part of osp(1|2), with the compact real form of osp(1|2) 0 . Explicitly they are given by J ‡ λ i := J i J ‡ λ 4 := (−1) λ J 5 (35) J ‡ λ 5 := (−1) λ+1 J 4 .

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“…With the condition (9), one classifies superfunctions as follows [19,24]. (9) holds, and we deal with H ∞ -superfunctions…”

Section: Supermanifoldsmentioning

confidence: 99%

“…In particular, the transformations of K corresponding to the left and right translations (19) are ordinary left and right multiplications of K by g.…”

Section: Superbundlesmentioning

confidence: 99%

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Supermetrics on Supermanifolds

Sardanashvily

2008

Int. J. Geom. Methods Mod. Phys.

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By virtue of the well-known theorem, a structure Lie group K of a principal bundle P → X is reducible to its closed subgroup H iff there exists a global section of the quotient bundle P/K → X. In gauge theory, such sections are treated as Higgs fields, exemplified by pseudoRiemannian metrics on a base manifold X. Under some conditions, this theorem is extended to principal superbundles in the category of G-supermanifolds. Given a G-supermanifold M and a graded frame superbundle over M with a structure general linear supergroup, a reduction of this structure supergroup to an orthgonal-symplectic supersubgroup is associated to a supermetric on a G-supermanifold M .

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Basic geometry of G-supermanifolds

Cited by 10 publications

References 0 publications

Synthesis and Characterization of Some Aza[5]helicenes

Synthesis and Characterization of Some Aza[5]helicenes

The fuzzy supersphere

Supermetrics on Supermanifolds

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