Deformations in Mathematics and Physics

Fialowski, Alice

doi:10.1007/s10773-007-9454-7

Cited by 4 publications

(4 citation statements)

References 19 publications

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“…One should note that g(−1) = iso(1, 1) and that l(0) = iso (2). For more information on low-dimensional Lie algebras and their contractions see for example [4,21,22,23,24].…”

Section: Our Notationmentioning

confidence: 99%

Strong contraction of the representations of the three-dimensional Lie algebras

Subag¹,

Baruch²,

Birman³

et al. 2012

J. Phys. A: Math. Theor.

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For anyİnönü-Wigner contraction of a three dimensional Lie algebra we construct the corresponding contractions of representations. Our method is quite canonical in the sense that in all cases we deal with realizations of the representations on some spaces of functions; we contract the differential operators on those spaces along with the representation spaces themselves by taking certain pointwise limit of functions. We call such contractions strong contractions. We show that this pointwise limit gives rise to a direct limit space. Many of these contractions are new and in other examples we give a different proof.

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“…One should note that g(−1) = iso(1, 1) and that l(0) = iso (2). For more information on low-dimensional Lie algebras and their contractions see for example [4,21,22,23,24].…”

Section: Our Notationmentioning

confidence: 99%

Strong contraction of the representations of the three-dimensional Lie algebras

Subag¹,

Baruch²,

Birman³

et al. 2012

J. Phys. A: Math. Theor.

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“…This way we get a richer picture about the original object itself [7]. But there is also another question approached via deformation.…”

Section: Introductionmentioning

confidence: 99%

Infinitesimal deformations of null-filiform Leibniz superalgebras

Khudoyberdiyev

Omirov

2013

Journal of Geometry and Physics

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Abstract. In this paper we describe the infinitesimal deformations of null-filiform Leibniz superalgebras over a field of zero characteristic. It is known that up to isomorphism in each dimension there exist two such superalgebras N F n,m . One of them is a Leibniz algebra (that is m = 0) and the second one is a pure Leibniz superalgebra (that is m = 0) of maximum nilindex. We show that the closure of union of orbits of single-generated Leibniz algebras forms an irreducible component of the variety of Leibniz algebras. We prove that any single-generated Leibniz algebra is a linear integrable deformation of the algebra N F n . Similar results for the case of Leibniz superalgebras are obtained.

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“…In mathematics, deformations of Lie algebra structures have been extensively studied since the fundamental works of Gerstenhaber, see [13], Nijenhuis and Richardson, see [24], [26] and are still objects of current research, see, in particular, [9], [10], [11].…”

Section: Introductionmentioning

confidence: 99%