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Journal articles on the topic 'Formal deformations'

Author: Grafiati

Published: 10 March 2023

Last updated: 31 July 2025

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1

Fialowski, Alice, and Michael Penkava. "On singular formal deformations." Archiv der Mathematik 106, no. 5 (2016): 431–38. http://dx.doi.org/10.1007/s00013-016-0894-2.

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2

Blanc, Anthony, Ludmil Katzarkov, and Pranav Pandit. "Generators in formal deformations of categories." Compositio Mathematica 154, no. 10 (2018): 2055–89. http://dx.doi.org/10.1112/s0010437x18007303.

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In this paper we use the theory of formal moduli problems developed by Lurie in order to study the space of formal deformations of a$k$-linear$\infty$-category for a field$k$. Our main result states that if${\mathcal{C}}$is a$k$-linear$\infty$-category which has a compact generator whose groups of self-extensions vanish for sufficiently high positive degrees, then every formal deformation of${\mathcal{C}}$has zero curvature and moreover admits a compact generator.

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3

Keller, Frank, and Stefan Waldmann. "Formal deformations of Dirac structures." Journal of Geometry and Physics 57, no. 3 (2007): 1015–36. http://dx.doi.org/10.1016/j.geomphys.2006.08.005.

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4

Grinberg, M., and D. Kazhdan. "Versal deformations of formal arcs." Geometric and Functional Analysis 10, no. 3 (2000): 543–55. http://dx.doi.org/10.1007/pl00001628.

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5

Huebschmann, Johannes. "The formal Kuranishi parameterization via the universal homological perturbation theory solution of the deformation equation." Georgian Mathematical Journal 25, no. 4 (2018): 529–44. http://dx.doi.org/10.1515/gmj-2018-0054.

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AbstractUsing homological perturbation theory, we develop a formal version of the miniversal deformation associated with a deformation problem controlled by a differential graded Lie algebra over a field of characteristic zero. Our approach includes a formal version of the Kuranishi method in the theory of deformations of complex manifolds.

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6

BOURQUI, DAVID, and JULIEN SEBAG. "DEFORMATIONS OF DIFFERENTIAL ARCS." Bulletin of the Australian Mathematical Society 94, no. 3 (2016): 405–10. http://dx.doi.org/10.1017/s0004972716000459.

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Let$k$be field of characteristic zero. Let$f\in k[X,Y]$be a nonconstant polynomial. We prove that the space of differential (formal) deformations of any formal general solution of the associated ordinary differential equation$f(y^{\prime },y)=0$is isomorphic to the formal disc$\text{Spf}(k[[Z]])$.

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7

Remm, Elisabeth. "Deformation Quantization of Nonassociative Algebras." Mathematics 13, no. 1 (2024): 58. https://doi.org/10.3390/math13010058.

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We investigate formal deformations of certain classes of nonassociative algebras including classes of K[Σ3]-associative algebras, Lie-admissible algebras and anti-associative algebras. In a process which is similar to Poisson algebra for the associative case, we identify for each type of algebras (A,μ) a type of algebras (A,μ,ψ) such that formal deformations of (A,μ) appear as quantizations of (A,μ,ψ). The process of polarization/depolarization associates to each nonassociative algebra a couple of algebras which products are respectively commutative and skew-symmetric and it is linked with the

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8

DEMCHENKO, OLEG, and ALEXANDER GUREVICH. "GROUP ACTION ON THE DEFORMATIONS OF A FORMAL GROUP OVER THE RING OF WITT VECTORS." Nagoya Mathematical Journal 235 (December 20, 2017): 42–57. http://dx.doi.org/10.1017/nmj.2017.43.

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A recent result by the authors gives an explicit construction for a universal deformation of a formal group $\unicode[STIX]{x1D6F7}$ of finite height over a finite field $k$ . This provides in particular a parametrization of the set of deformations of $\unicode[STIX]{x1D6F7}$ over the ring ${\mathcal{O}}$ of Witt vectors over $k$ . Another parametrization of the same set can be obtained through the Dieudonné theory. We find an explicit relation between these parameterizations. As a consequence, we obtain an explicit expression for the action of $\text{Aut}_{k}(\unicode[STIX]{x1D6F7})$ on the s

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9

Miyajima, Kimio. "ANALYTIC APPROACH TO DEFORMATION OF RESOLUTION OF NORMAL ISOLATED SINGULARITIES: FORMAL DEFORMATIONS." Journal of the Korean Mathematical Society 40, no. 4 (2003): 709–25. http://dx.doi.org/10.4134/jkms.2003.40.4.709.

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10

Tang, Rong, Yunhe Sheng, and Yanqiu Zhou. "Deformations of relative Rota–Baxter operators on Leibniz algebras." International Journal of Geometric Methods in Modern Physics 17, no. 12 (2020): 2050174. http://dx.doi.org/10.1142/s0219887820501741.

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In this paper, we introduce the cohomology theory of relative Rota–Baxter operators on Leibniz algebras. We use the cohomological approach to study linear and formal deformations of relative Rota–Baxter operators. In particular, the notion of Nijenhuis elements is introduced to characterize trivial linear deformations. Formal deformations and extendibility of order [Formula: see text] deformations of a relative Rota–Baxter operator are also characterized in terms of the cohomology theory.

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11

Elhamdadi, Mohamed, and Abdenacer Makhlouf. "Cohomology and Formal Deformations of Alternative Algebras." Journal of Generalized Lie Theory and Applications 5 (2011): 1–10. http://dx.doi.org/10.4303/jglta/g110105.

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12

Chouhy, Sergio. "On geometric degenerations and Gerstenhaber formal deformations." Bulletin of the London Mathematical Society 51, no. 5 (2019): 787–97. http://dx.doi.org/10.1112/blms.12277.

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13

Karabegov, Alexander. "Infinitesimal Deformations of a Formal Symplectic Groupoid." Letters in Mathematical Physics 97, no. 3 (2011): 279–301. http://dx.doi.org/10.1007/s11005-011-0495-8.

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14

Stancu, Alin. "On some constructions of nil-clean, clean and exchange rings." Journal of Algebra and Its Applications 14, no. 07 (2015): 1550101. http://dx.doi.org/10.1142/s0219498815501017.

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In this paper, we discuss several constructions that lead to new examples of nil-clean, clean and exchange rings. Extensions by ideals contained in the Jacobson radical is the common theme of these constructions. A characterization of the idempotents in the algebra defined by a 2-cocycle is given and used to prove some of the algebra's properties (the infinitesimal deformation case). From infinitesimal deformations, we go to full deformations and prove that any formal deformation of a clean (exchange) ring is itself clean (exchange). Examples of nil-clean, clean and exchange rings, arising fro

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15

Abdaoui, K., R. Gharbi, S. Mabrouk, and A. Makhlouf. "Cohomology and formal deformations of n -Hom–Lie color algebras." Ukrains’kyi Matematychnyi Zhurnal 75, no. 9 (2023): 1155–77. http://dx.doi.org/10.3842/umzh.v75i9.7238.

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UDC 512.5 The aim of this paper is to provide a cohomology of n -Hom–Lie color algebras, in particular, a cohomology governing one-parameter formal deformations. Then we also study formal deformations of the n -Hom–Lie color algebras and introduce the notion of Nijenhuis operator on a n -Hom–Lie color algebra, which may give rise to infinitesimally trivial ( n - 1 ) -order deformations. Furthermore, in connection with Nijenhuis operators, we introduce and discuss the notion of product structure on n -Hom–Lie color algebras.

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16

Zhao, Jia, and Yu Qiao. "Cohomology and Deformations of Relative Rota–Baxter Operators on Lie-Yamaguti Algebras." Mathematics 12, no. 1 (2024): 166. http://dx.doi.org/10.3390/math12010166.

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In this paper, we establish the cohomology of relative Rota–Baxter operators on Lie-Yamaguti algebras via the Yamaguti cohomology. Then, we use this type of cohomology to characterize deformations of relative Rota–Baxter operators on Lie-Yamaguti algebras. We show that if two linear or formal deformations of a relative Rota–Baxter operator are equivalent, then their infinitesimals are in the same cohomology class in the first cohomology group. Moreover, an order n deformation of a relative Rota–Baxter operator can be extended to an order n+1 deformation if and only if the obstruction class in

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17

Greilhuber, Josef. "Holomorphic support functions for uniformly pseudoconvex hypersurfaces, with an application to CR maps." Proceedings of the American Mathematical Society, Series B 11, no. 15 (2024): 147–56. http://dx.doi.org/10.1090/bproc/222.

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We construct holomorphic support functions for smooth weakly pseudoconvex hypersurfaces with Levi form of constant rank. These are then applied to show that formal holomorphic curves which are tangential to infinite order to such a hypersurface must be formally contained in its Levi foliation. As a consequence, we obtain a holomorphic deformation theorem for nowhere smooth CR maps into smooth pseudoconvex hypersurfaces with one-dimensional Levi foliation, strengthening a very general result of Lamel and Mir about formal deformations in this particular case.

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18

Griffith, Phillip. "Induced formal deformations and the Cohen-Macaulay property." Transactions of the American Mathematical Society 353, no. 1 (2000): 77–93. http://dx.doi.org/10.1090/s0002-9947-00-02513-7.

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19

Lazarev, A. "Deformations of formal groups and stable homotopy theory." Topology 36, no. 6 (1997): 1317–31. http://dx.doi.org/10.1016/s0040-9383(96)00051-1.

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20

GUERRINI, L. "FORMAL AND ANALYTIC DEFORMATIONS FROM WITT TO VIRASORO." Reviews in Mathematical Physics 14, no. 03 (2002): 303–16. http://dx.doi.org/10.1142/s0129055x02001181.

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We introduce a new family [Formula: see text] of deformations of the Witt algebra [Formula: see text], F varying in the space of all polynomials with vanishing constant terms, and show the existence of an isomorphism of its formal and analytic completions with those of the Witt algebra. Central extensions of this algebra are considered and the existence of an isomorphism between their formal and analytic completions with those of the Virasoro algebra is proved.

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21

Pichereau, Anne. "Formal deformations of Poisson structures in low dimensions." Pacific Journal of Mathematics 239, no. 1 (2009): 105–33. http://dx.doi.org/10.2140/pjm.2009.239.105.

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22

Liu, Linlin, and Huihui Zheng. "Formal deformations of associative and Lie H-pseudoalgebras." ScienceAsia 49, no. 4 (2023): 576. http://dx.doi.org/10.2306/scienceasia1513-1874.2023.019.

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23

Kawamata, Yujiro. "On formal non-commutative deformations of smooth varieties." Advances in Mathematics 478 (October 2025): 110392. https://doi.org/10.1016/j.aim.2025.110392.

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24

Ma, Yao, Liangyun Chen, and Jie Lin. "One-parameter formal deformations of Hom-Lie-Yamaguti algebras." Journal of Mathematical Physics 56, no. 1 (2015): 011701. http://dx.doi.org/10.1063/1.4905733.

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25

Brown, Richard A. "Generalized group presentation and formal deformations of CW complexes." Transactions of the American Mathematical Society 334, no. 2 (1992): 519–49. http://dx.doi.org/10.1090/s0002-9947-1992-1153010-3.

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26

Fialowski, Alice, and Michael Penkava. "Formal Deformations, Contractions and Moduli Spaces of Lie Algebras." International Journal of Theoretical Physics 47, no. 2 (2007): 561–82. http://dx.doi.org/10.1007/s10773-007-9481-4.

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27

Green, Barry. "Realizing deformations of curves using Lubin-Tate formal groups." Israel Journal of Mathematics 139, no. 1 (2004): 139–48. http://dx.doi.org/10.1007/bf02787544.

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28

Saha, Ripan. "Equivariant associative dialgebras and its one-parameter formal deformations." Journal of Geometry and Physics 146 (December 2019): 103491. http://dx.doi.org/10.1016/j.geomphys.2019.103491.

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29

Lecomte, P. B. A., and C. Roger. "Formal deformations of the associative algebra of smooth matrices." Letters in Mathematical Physics 15, no. 1 (1988): 55–63. http://dx.doi.org/10.1007/bf00416572.

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30

Das, Apurba. "Cohomology and deformations of weighted Rota–Baxter operators." Journal of Mathematical Physics 63, no. 9 (2022): 091703. http://dx.doi.org/10.1063/5.0093066.

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Weighted Rota–Baxter operators on associative algebras are closely related to modified Yang–Baxter equations, splitting of algebras, and weighted infinitesimal bialgebras and play an important role in mathematical physics. For any λ ∈ k, we construct a differential graded Lie algebra whose Maurer–Cartan elements are given by λ-weighted relative Rota–Baxter operators. Using such characterization, we define the cohomology of a λ-weighted relative Rota-Baxter operator T and interpret this as the Hochschild cohomology of a suitable algebra with coefficients in an appropriate bimodule. We study lin

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31

BIELIAVSKY, PIERRE, and PHILIPPE BONNEAU. "ON THE GEOMETRY OF THE CHARACTERISTIC CLASS OF A STAR PRODUCT ON A SYMPLECTIC MANIFOLD." Reviews in Mathematical Physics 15, no. 02 (2003): 199–215. http://dx.doi.org/10.1142/s0129055x0300159x.

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The characteristic class of a star product on a symplectic manifold appears as the class of a deformation of a given symplectic connection, as described by Fedosov. In contrast, one usually thinks of the characteristic class of a star product as the class of a deformation of the Poisson structure (as in Kontsevich's work). In this paper, we present, in the symplectic framework, a natural procedure for constructing a star product by directly quantizing a deformation of the symplectic structure. Basically, in Fedosov's recursive formula for the star product with zero characteristic class, we rep

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32

Basdouri, Khaled, та Salem Omri. "Cohomology and deformation of 𝔞𝔣𝔣(1|1) acting on differential operators". International Journal of Geometric Methods in Modern Physics 15, № 05 (2018): 1850072. http://dx.doi.org/10.1142/s021988781850072x.

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We consider the [Formula: see text]-module structure on the spaces of differential operators acting on the spaces of weighted densities. We compute the second differential cohomology of the Lie superalgebra [Formula: see text] with coefficients in differential operators acting on the spaces of weighted densities. We classify formal deformations of the [Formula: see text]-module structure on the superspaces of symbols of differential operators. We prove that any formal deformation of a given infinitesimal deformation of this structure is equivalent to its infinitesimal part. This work is the si

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33

Zhu, Yifei. "Norm coherence for descent of level structures on formal deformations." Journal of Pure and Applied Algebra 224, no. 10 (2020): 106382. http://dx.doi.org/10.1016/j.jpaa.2020.106382.

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34

ZHAO, WENHUA. "DEFORMATIONS AND INVERSION FORMULAS FOR FORMAL AUTOMORPHISMS IN NONCOMMUTATIVE VARIABLES." International Journal of Algebra and Computation 17, no. 02 (2007): 261–88. http://dx.doi.org/10.1142/s0218196707003676.

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Let z = (z1, z2,…, zn) be noncommutative free variables and t a formal parameter which commutes with z. Let k be any unital integral domain of any characteristic and Ft(z) = z - Ht(z) with Ht(z) ∈ k[[t]]〈〈z〉〉×n and the order o(Ht(z))≥ 2. Note that Ft(z) can be viewed as a deformation of the formal map F(z):= z - Ht=1(z) when it makes sense (for example, when Ht(z) ∈ k[t]〈〈z〉〉×n). The inverse map Gt(z) of Ft(z) can always be written as Gt(z) = z+Mt(z) with Mt(z) ∈ k[[t]]〈〈z〉〉×n and o(Mt(z)) ≥ 2. In this paper, we first derive the PDEs satisfied by Mt(z) and u(Ft), u(Gt) ∈ k[[t]]〈〈z〉〉 with u(z)

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35

Bremer, Christopher L., and Daniel S. Sage. "Isomonodromic Deformations of Connections with Singularities of Parahoric Formal Type." Communications in Mathematical Physics 313, no. 1 (2012): 175–208. http://dx.doi.org/10.1007/s00220-012-1493-0.

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36

FIALOWSKI, ALICE, and MARTIN SCHLICHENMAIER. "GLOBAL DEFORMATIONS OF THE WITT ALGEBRA OF KRICHEVER–NOVIKOV TYPE." Communications in Contemporary Mathematics 05, no. 06 (2003): 921–45. http://dx.doi.org/10.1142/s0219199703001208.

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By considering non-trivial global deformations of the Witt (and the Virasoro) algebra given by geometric constructions it is shown that, despite their infinitesimal and formal rigidity, they are globally not rigid. This shows the need of a clear indication of the type of deformations considered. The families appearing are constructed as families of algebras of Krichever–Novikov type. They show up in a natural way in the global operator approach to the quantization of two-dimensional conformal field theory. In addition, a proof of the infinitesimal and formal rigidity of the Witt algebra is pre

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37

GUERRINI, LUCA. "FORMAL AND ANALYTIC RIGIDITY OF THE WITH ALGEBRA." Reviews in Mathematical Physics 11, no. 03 (1999): 303–20. http://dx.doi.org/10.1142/s0129055x99000118.

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A family of deformations [Formula: see text] of the Witt algebra [Formula: see text] parametrized by the space ℰ of even polynomials with vanishing constant terms is defined. The existence of an isomorphism [Formula: see text], where [Formula: see text] refers to suitable completions of [Formula: see text], is proved. A relation between [Formula: see text] and Krichever–Novikov algebras of genus 0 and 1 is given.

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38

FRONSDAL, CHRISTIAN. "DEFORMATION QUANTIZATION: IS C1 NECESSARILY SKEW?" International Journal of Modern Physics B 16, no. 14n15 (2002): 1925–30. http://dx.doi.org/10.1142/s0217979202011640.

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Deformation quantization (of a commutative algebra) is based on the introduction of a new associative product, expressed as a formal series, [Formula: see text]. In the case of the algebra of functions on a symplectic space the first term in the perturbation is often identified with the antisymmetric Poisson bracket. There is a wide-spread belief that every associative *-product is equivalent to one for which C1(f,g) is antisymmetric and that, in particular, every abelian deformation is trivial. This paper shows that this is far from being the case and illustrates the existence of abelian defo

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39

Baklouti, A., N. Elaloui, and I. Kedim. "The Selberg–Weil–Kobayashi rigidity theorem: The rank one solvable case." International Journal of Mathematics 27, no. 10 (2016): 1650085. http://dx.doi.org/10.1142/s0129167x16500853.

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A local rigidity theorem was proved by Selberg and Weil for Riemannian symmetric spaces and generalized by Kobayashi for a non-Riemannian homogeneous space [Formula: see text], determining explicitly which homogeneous spaces [Formula: see text] allow nontrivial continuous deformations of co-compact discontinuous groups. When [Formula: see text] is assumed to be exponential solvable and [Formula: see text] is a maximal subgroup, an analog of such a theorem states that the local rigidity holds if and only if [Formula: see text] is isomorphic to the group Aff([Formula: see text]) of affine transf

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40

Khalfoun, Hafedh, Nizar Ben Fraj та Meher Abdaoui. "Cohomology of 𝔞𝔣𝔣(m|1) acting on the space of superpseudodifferential operators on the supercircle S1|m". Asian-European Journal of Mathematics 11, № 04 (2018): 1850057. http://dx.doi.org/10.1142/s1793557118500572.

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We investigate the first differential cohomology space associated with the embedding of the affine Lie superalgebra [Formula: see text] on the [Formula: see text]-dimensional supercircle [Formula: see text] in the Lie superalgebra [Formula: see text] of superpseudodifferential operators with smooth coefficients, where [Formula: see text]. Following Ovsienko and Roger, we give explicit expressions of the basis cocycles. We study the deformations of the structure of the [Formula: see text]-module [Formula: see text]. We prove that any formal deformation is equivalent to its infinitesimal part.

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41

Collin, Annabelle, Sébastien Imperiale, Philippe Moireau, Jean-Frédéric Gerbeau, and Dominique Chapelle. "Apprehending the effects of mechanical deformations in cardiac electrophysiology: A homogenization approach." Mathematical Models and Methods in Applied Sciences 29, no. 13 (2019): 2377–417. http://dx.doi.org/10.1142/s0218202519500490.

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We follow a formal homogenization approach to investigate the effects of mechanical deformations in electrophysiology models relying on a bidomain description of ionic motion at the microscopic level. To that purpose, we extend these microscopic equations to take into account the mechanical deformations, and proceed by recasting the problem in the framework of classical two-scale homogenization in periodic media, and identifying the equations satisfied by the first coefficients in the formal expansions. The homogenized equations reveal some interesting effects related to the microstructure — a

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42

Bäck, P. "Notes on formal deformations of quantum planes and universal enveloping algebras." Journal of Physics: Conference Series 1194 (April 2019): 012011. http://dx.doi.org/10.1088/1742-6596/1194/1/012011.

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43

Müller, Gerd. "Deformations of reductive group actions." Mathematical Proceedings of the Cambridge Philosophical Society 106, no. 1 (1989): 77–88. http://dx.doi.org/10.1017/s0305004100067992.

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Consider actions of a reductive complex Lie group G on an analytic space germ (X, 0). In a previous paper [16] we proved that such an action is determined uniquely (up to conjugation with an automorphism of (X, 0)) by the induced action of G on the tangent space of (X, 0). Here it will be shown that every deformation of such an action, parametrized holomorphically by a reduced analytic space germ, is trivial, i.e. can be obtained from the given action by conjugation with a family of automorphisms of (X, 0) depending holomorphically on the parameter. (For a more precise formulation in terms of

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44

Li, Qiang, and Lili Ma. "1-parameter formal deformations and abelian extensions of Lie color triple systems." Electronic Research Archive 30, no. 7 (2022): 2524–39. http://dx.doi.org/10.3934/era.2022129.

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<abstract><p>The purpose of this paper is to discuss Lie color triple systems. The cohomology theory of Lie color triple systems is established, then 1-parameter formal deformations and abelian extensions of Lie color triple systems are studied using cohomology.</p></abstract>

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45

Choie, YoungJu, François Dumas, François Martin, and Emmanuel Royer. "Formal deformations of the algebra of Jacobi forms and Rankin–Cohen brackets." Comptes Rendus. Mathématique 359, no. 4 (2021): 505–21. http://dx.doi.org/10.5802/crmath.193.

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46

Kawamata, Yujiro. "On non-commutative formal deformations of coherent sheaves on an algebraic variety." EMS Surveys in Mathematical Sciences 8, no. 1 (2021): 237–63. http://dx.doi.org/10.4171/emss/49.

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47

Lychev, S. A., K. G. Koifman, and A. V. Digilov. "NONLINEAR DYNAMIC EQUATIONS FOR ELASTIC MICROMORPHIC SOLIDS AND SHELLS. PART I." Vestnik of Samara University. Natural Science Series 27, no. 1 (2021): 81–103. http://dx.doi.org/10.18287/2541-7525-2021-27-1-81-103.

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The present paper develops a general approach to deriving nonlinear equations of motion for solids whose material points possess additional degrees of freedom. The essential characteristic of this approach is theaccount of incompatible deformations that may occur in the body due to distributed defects or in the result of the some kind of process like growth or remodelling. The mathematical formalism is based on least action principle and Noether symmetries. The peculiarity of such formalism is in formal description of reference shape of the body, which in the case of incompatible deformations

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48

Liu, Shanshan, Abdenacer Makhlouf, and Lina Song. "The full cohomology, abelian extensions and formal deformations of Hom-pre-Lie algebras." Electronic Research Archive 30, no. 8 (2022): 2748–73. http://dx.doi.org/10.3934/era.2022141.

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<abstract><p>The main purpose of this paper is to provide a full cohomology of a Hom-pre-Lie algebra with coefficients in a given representation. This new type of cohomology exploits strongly the Hom-type structure and fits perfectly with simultaneous deformations of the multiplication and the homomorphism defining a Hom-pre-Lie algebra. Moreover, we show that its second cohomology group classifies abelian extensions of a Hom-pre-Lie algebra by a representation.</p></abstract>

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49

GUERRINI, L. "COMPLETIONS OF 2-TORSION KN-ALGEBRAS OF GENUS 1." Reviews in Mathematical Physics 13, no. 02 (2001): 253–66. http://dx.doi.org/10.1142/s0129055x01000648.

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Krichever–Novikov algebras [Formula: see text] of genus 1 with markings which are two 2-torsion points are related to a family [Formula: see text] of deformations of the Witt algebra [Formula: see text], where f varies in the space of even polynomials with vanishing constant terms. An isomorphism between the formal (resp. analytic) completion of these KN-algebras with those of the Witt algebra is proved. Central extensions of these algebras are also defined and their formal completion is proved to be isomorphic to that of the Virasoro algebra Vir.

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50

Argyriadis, Ion. "The superposed orogenesis of the alpine-mediterranean edifice." Boletín Geológico y Minero 127, no. 2-3 (2016): 593–612. http://dx.doi.org/10.21701/bolgeomin.127.2-3.020.

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The circum-Mediterranean chains must be considered as the result of two distinct orogenies. The apparent unity of the present structure is of formal order, due to the latest deformations. Since the Hercynian time there have been two periods of paroxysmal deformation; the younger fits the definition of the alpine orogeny; the older occurred during the Cretaceous and may correspond to the first great convergent relative drift of the Eurasiatic and African blocks. The Cretaceous or Mesogean orogeny is independent from the Alpine orogeny stricto sensu (Oligo-Miocene) and cannot be considered as it

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