Deformations of Complex Structures on a Real Lie Algebra

1993 ◽  
pp. 377-385
Author(s):  
Giuliana Gigante ◽  
Giuseppe Tomassini
Keyword(s):  
Lie Algebra ◽  
Complex Structures ◽  
Deformations Of Complex Structures

A Criterion for Versality Of Deformations of Tubular Neighborhoods of Strongly Pseudo Convex Boundaries

1992 ◽  
Vol 44 (2) ◽  
pp. 225-233
Author(s):  
Takao Akahori
Keyword(s):  
Completeness Theorem ◽  
Complex Structures ◽  
Tubular Neighborhoods ◽  
Deformations Of Complex Structures ◽  
Pseudo Convex

AbstractWe extend the famous Kodaira-Spencer's completeness theorem for a family of deformations of complex structures (see [12]). As an application, we show that the canonical family constructed in [9] is versai.

scholarly journals Geometry of logarithmic forms and deformations of complex structures

2019 ◽  
Vol 28 (4) ◽  
pp. 773-815 ◽  
Author(s):  
Kefeng Liu ◽  
Sheng Rao ◽  
Xueyuan Wan
Keyword(s):  
Complex Structures ◽  
Deformations Of Complex Structures

scholarly journals About Zero Torsion Linear Maps on Lie Algebras

ISRN Algebra ◽  
2011 ◽  
Vol 2011 ◽  
pp. 1-16
Author(s):  
Louis Magnin
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Equivalence Classes ◽  
Explicit Description ◽  
Complex Structures ◽  
Linear Map ◽  
3 Dimensional ◽  
Linear Maps

We prove that any zero torsion linear map on a nonsolvable real Lie algebra is an extension of some CR-structure. We then study the cases of (2, ) and the 3-dimensional Heisenberg Lie algebra . In both cases, we compute up to equivalence all zero torsion linear maps on , and deduce an explicit description of the equivalence classes of integrable complex structures on .

scholarly journals Complex structures on the complexification of a real Lie algebra

2018 ◽  
Vol 5 (1) ◽  
pp. 150-157
Author(s):  
Takumi Yamada
Keyword(s):  
Lie Algebra ◽  
Complex Structure ◽  
Complex Structures ◽  
Direct Sum ◽  
Direct Sum Decomposition

AbstractLet g = a+b be a Lie algebra with a direct sum decomposition such that a and b are Lie subalgebras. Then, we can construct an integrable complex structure J̃ on h = ℝ(gℂ) from the decomposition, where ℝ(gℂ) is a real Lie algebra obtained from gℂby the scalar restriction. Conversely, let J̃ be an integrable complex structure on h = ℝ(gℂ). Then, we have a direct sum decomposition g = a + b such that a and b are Lie subalgebras. We also investigate relations between the decomposition g = a + b and dim Hs.t∂̄J̃ (hℂ).

scholarly journals VB-Courant Algebroids, E-Courant Algebroids and Generalized Geometry

2018 ◽  
Vol 61 (3) ◽  
pp. 588-607 ◽  
Author(s):  
Honglei Lang ◽  
Yunhe Sheng ◽  
Aïssa Wade
Keyword(s):  
Lie Algebra ◽  
Complex Structure ◽  
Contact Structures ◽  
Complex Structures ◽  
Courant Algebroids ◽  
Courant Algebroid ◽  
Generalized Complex Structures ◽  
Generalized Complex Structure ◽  
Generalized Geometry ◽  
Generalized Complex

AbstractIn this paper, we first discuss the relation between VB-Courant algebroids and E-Courant algebroids, and we construct some examples of E-Courant algebroids. Then we introduce the notion of a generalized complex structure on an E-Courant algebroid, unifying the usual generalized complex structures on even-dimensional manifolds and generalized contact structures on odd-dimensional manifolds. Moreover, we study generalized complex structures on an omni-Lie algebroid in detail. In particular, we show that generalized complex structures on an omni-Lie algebra gl(V) ⊕ V correspond to complex Lie algebra structures on V.

scholarly journals Extending invariant complex structures

2015 ◽  
Vol 26 (11) ◽  
pp. 1550096 ◽  
Author(s):  
Rutwig Campoamor Stursberg ◽  
Isolda E. Cardoso ◽  
Gabriela P. Ovando
Keyword(s):  
Lie Algebra ◽  
Algebraic Structure ◽  
Symplectic Structure ◽  
Complex Structure ◽  
Complex Structures ◽  
Additional Structure ◽  
Totally Real

We study the problem of extending a complex structure to a given Lie algebra 𝔤, which is firstly defined on an ideal 𝔥 ⊂ 𝔤. We consider the next situations: 𝔥 is either complex or it is totally real. The next question is to equip 𝔤 with an additional structure, such as a (non)-definite metric or a symplectic structure and to ask either 𝔥 is non-degenerate, isotropic, etc. with respect to this structure, by imposing a compatibility assumption. We show that this implies certain constraints on the algebraic structure of 𝔤. Constructive examples illustrating this situation are shown, in particular computations in dimension six are given.

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