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Journal articles on the topic 'Nijenhuis'

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Author: Grafiati

Published: 10 March 2023

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1

Gozzi, E., and D. Mauro. "A new look at the Schouten–Nijenhuis, Frölicher–Nijenhuis, and Nijenhuis–Richardson brackets." Journal of Mathematical Physics 41, no. 4 (April 2000): 1916–33. http://dx.doi.org/10.1063/1.533218.

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2

Leroux, Philippe. "Construction of Nijenhuis operators and dendriform trialgebras." International Journal of Mathematics and Mathematical Sciences 2004, no. 49 (2004): 2595–615. http://dx.doi.org/10.1155/s0161171204402117.

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We construct Nijenhuis operators from particular bialgebras called dendriform-Nijenhuis bialgebras. It turns out that such Nijenhuis operators commute withTD-operators, a kind of Baxter-Rota operators, and are therefore closely related to dendriform trialgebras. This allows the construction of associative algebras, called dendriform-Nijenhuis algebras, made out of nine operations and presenting an exotic combinatorial property. We also show that the augmented free dendriform-Nijenhuis algebra and its commutative version have a structure of connected Hopf algebras. Examples are given.

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3

Bolsinov, Alexey V., Andrey Yu Konyaev, and Vladimir S. Matveev. "Nijenhuis geometry." Advances in Mathematics 394 (January 2022): 108001. http://dx.doi.org/10.1016/j.aim.2021.108001.

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4

Liu, Jiefeng, Sihan Zhou, and Lamei Yuan. "Conformal r-matrix-Nijenhuis structures, symplectic-Nijenhuis structures, and ON-structures." Journal of Mathematical Physics 63, no. 10 (October 1, 2022): 101701. http://dx.doi.org/10.1063/5.0101471.

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In this paper, we first study infinitesimal deformations of a Lie conformal algebra and a Lie conformal algebra with a module (called an [Formula: see text] pair), which lead to the notions of the Nijenhuis operator on the Lie conformal algebra and the Nijenhuis structure on the [Formula: see text] pair, respectively. Then, by adding compatibility conditions between Nijenhuis structures and [Formula: see text]-operators, we introduce the notion of an [Formula: see text]-structure on an [Formula: see text] pair and show that an [Formula: see text]-structure gives rise to a hierarchy of pairwise compatible [Formula: see text]-operators. In particular, we show that compatible [Formula: see text]-operators on a Lie conformal algebra can be characterized by Nijenhuis operators on Lie conformal algebras. Finally, we introduce the notions of the conformal r-matrix-Nijenhuis structure and symplectic-Nijenhuis structure on Lie conformal algebras and study their relations.

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5

CORDEIRO, FLÁVIO, and JOANA M. NUNES DA COSTA. "REDUCTION AND CONSTRUCTION OF POISSON QUASI-NIJENHUIS MANIFOLDS WITH BACKGROUND." International Journal of Geometric Methods in Modern Physics 07, no. 04 (June 2010): 539–64. http://dx.doi.org/10.1142/s0219887810004439.

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We extend the Falceto–Zambon version of Marsden–Ratiu Poisson reduction to Poisson quasi-Nijenhuis structures with background on manifolds. We define gauge transformations of Poisson quasi-Nijenhuis structures with background, study some of their properties and show that they are compatible with reduction procedure. We use gauge transformations to construct Poisson quasi-Nijenhuis structures with background.

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6

Wang, Qi, Jiefeng Liu, and Yunhe Sheng. "Koszul–Vinberg structures and compatible structures on left-symmetric algebroids." International Journal of Geometric Methods in Modern Physics 17, no. 13 (October 13, 2020): 2050199. http://dx.doi.org/10.1142/s0219887820501996.

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In this paper, we introduce the notion of Koszul–Vinberg–Nijenhuis (KVN) structures on a left-symmetric algebroid as analogues of Poisson–Nijenhuis structures on a Lie algebroid, and show that a KVN-structure gives rise to a hierarchy of Koszul–Vinberg structures. We introduce the notions of [Formula: see text]-structures, pseudo-Hessian–Nijenhuis structures and complementary symmetric [Formula: see text]-tensors for Koszul–Vinberg structures on left-symmetric algebroids, which are analogues of [Formula: see text]-structures, symplectic-Nijenhuis structures and complementary [Formula: see text]-forms for Poisson structures. We also study the relationships between these various structures.

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7

Wang, Qi, Yunhe Sheng, Chengming Bai, and Jiefeng Liu. "Nijenhuis operators on pre-Lie algebras." Communications in Contemporary Mathematics 21, no. 07 (October 10, 2019): 1850050. http://dx.doi.org/10.1142/s0219199718500505.

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First we use a new approach to define a graded Lie algebra whose Maurer–Cartan elements characterize pre-Lie algebra structures. Then using this graded Lie bracket, we define the notion of a Nijenhuis operator on a pre-Lie algebra which generates a trivial deformation of this pre-Lie algebra. There are close relationships between [Formula: see text]-operators, Rota–Baxter operators and Nijenhuis operators on a pre-Lie algebra. In particular, a Nijenhuis operator “connects” two [Formula: see text]-operators on a pre-Lie algebra whose any linear combination is still an [Formula: see text]-operator in certain sense and hence compatible [Formula: see text]-dendriform algebras appear naturally as the induced algebraic structures. For the case of the dual representation of the regular representation of a pre-Lie algebra, there is a geometric interpretation by introducing the notion of a pseudo-Hessian–Nijenhuis structure which gives rise to a sequence of pseudo-Hessian and pseudo-Hessian–Nijenhuis structures. Another application of Nijenhuis operators on pre-Lie algebras in geometry is illustrated by introducing the notion of a para-complex structure on a pre-Lie algebra and then studying para-complex quadratic pre-Lie algebras and para-complex pseudo-Hessian pre-Lie algebras in detail. Finally, we give some examples of Nijenhuis operators on pre-Lie algebras.

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8

De Nicola, Antonio, Juan Carlos Marrero, and Edith Padrón. "Reduction of Poisson–Nijenhuis Lie algebroids to symplectic-Nijenhuis Lie algebroids with a nondegenerate Nijenhuis tensor." Journal of Physics A: Mathematical and Theoretical 44, no. 42 (October 4, 2011): 425206. http://dx.doi.org/10.1088/1751-8113/44/42/425206.

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9

Norris, L. K. "Schouten–Nijenhuis brackets." Journal of Mathematical Physics 38, no. 5 (May 1997): 2694–709. http://dx.doi.org/10.1063/1.531981.

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10

Longguang, He, and Liu Baokang. "Dirac-Nijenhuis manifolds." Reports on Mathematical Physics 53, no. 1 (February 2004): 123–42. http://dx.doi.org/10.1016/s0034-4877(04)90008-0.

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11

Das, Apurba. "Poisson-Nijenhuis Groupoids." Reports on Mathematical Physics 84, no. 3 (December 2019): 303–31. http://dx.doi.org/10.1016/s0034-4877(19)30095-3.

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12

Clemente-Gallardo, J., and J. M. Nunes da Costa. "Dirac–Nijenhuis structures." Journal of Physics A: Mathematical and General 37, no. 29 (July 8, 2004): 7267–96. http://dx.doi.org/10.1088/0305-4470/37/29/007.

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13

ANTUNES, P., and J. M. NUNES DA COSTA. "FROM HYPERSYMPLECTIC STRUCTURES TO COMPATIBLE PAIRS OF TENSORS ON A LIE ALGEBROID." International Journal of Geometric Methods in Modern Physics 10, no. 08 (August 7, 2013): 1360005. http://dx.doi.org/10.1142/s0219887813600050.

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A hypersymplectic structure on a Lie algebroid determines several Poisson–Nijenhuis, ΩN and PΩ structures on that Lie algebroid. We show that these Poisson–Nijenhuis (respectively, ΩN, PΩ) structures on the Lie algebroid, are pairwise compatible.

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14

Witte, Toby. "Reactie op Herman Nijenhuis." Journal of Social Intervention: Theory and Practice 21, no. 3 (September 11, 2012): 81. http://dx.doi.org/10.18352/jsi.319.

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15

Sheng, Yunhe. "Jacobi quasi-Nijenhuis algebroids." Reports on Mathematical Physics 65, no. 2 (April 2010): 271–87. http://dx.doi.org/10.1016/s0034-4877(10)80021-7.

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16

Nakamura, Tomoya. "Pseudo-Poisson Nijenhuis Manifolds." Reports on Mathematical Physics 82, no. 1 (August 2018): 121–35. http://dx.doi.org/10.1016/s0034-4877(18)30074-0.

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17

Stiénon, Mathieu, and Ping Xu. "Poisson Quasi-Nijenhuis Manifolds." Communications in Mathematical Physics 270, no. 3 (January 9, 2007): 709–25. http://dx.doi.org/10.1007/s00220-006-0168-0.

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18

Konyaev, Andrey Yu. "Nijenhuis geometry II: Left-symmetric algebras and linearization problem for Nijenhuis operators." Differential Geometry and its Applications 74 (February 2021): 101706. http://dx.doi.org/10.1016/j.difgeo.2020.101706.

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19

Wicherts, Jelte M. "THIS (METHOD) IS (NOT) FINE." Journal of Biosocial Science 50, no. 6 (July 17, 2018): 872–74. http://dx.doi.org/10.1017/s0021932018000184.

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SummaryIn their response to my criticism of their recent article in Journal of Biosocial Science (te Nijenhuis et al., 2017), te Nijenhuis and van den Hoek (2018) raise four points none of which concerns my main point that the method of correlated vectors (MCV) applied to item-level data represents a flawed method. Here, I discuss te Nijenhuis and van den Hoek’s four points. First, I argue that my previous application of MCV to item-level data showed that the method can yield nonsensical results. Second, I note that meta-analytic corrections for sampling error, imperfect measures, restriction of range and unreliability of the vectors are futile and cannot help fix the method. Third, I note that even with perfect data, the method can yield negative correlations. Fourth, I highlight the irrelevance of te Nijenhuis and van den Hoek (2018)’s point that my comment had not been published in a peerreviewed journal by referring to my articles in 2009 and 2017 on MCV in peer-reviewed journals.

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20

Tempesta, Piergiulio, and Giorgio Tondo. "Higher Haantjes Brackets and Integrability." Communications in Mathematical Physics 389, no. 3 (November 2, 2021): 1647–71. http://dx.doi.org/10.1007/s00220-021-04233-5.

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AbstractWe propose a new, infinite class of brackets generalizing the Frölicher–Nijenhuis bracket. This class can be reduced to a family of generalized Nijenhuis torsions recently introduced. In particular, the Haantjes bracket, the first example of our construction, is relevant in the characterization of Haantjes moduli of operators. We also prove that the vanishing of a higher-level Nijenhuis torsion of an operator field is a sufficient condition for the integrability of its eigen-distributions. This result (which does not require any knowledge of the spectral properties of the operator) generalizes the celebrated Haantjes theorem. The same vanishing condition also guarantees that the operator can be written, in a local chart, in a block-diagonal form.

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21

Li, Qiang, and Lili Ma. "Nijenhuis Operators and Abelian Extensions of Hom-δ-Jordan Lie Supertriple Systems." Mathematics 11, no. 4 (February 8, 2023): 871. http://dx.doi.org/10.3390/math11040871.

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Representations and cohomologies of Hom-δ-Jordan Lie supertriple systems are established. As an application, Nijenhuis operators and abelian extensions of Hom-δ-Jordan Lie supertriple systems are discussed. We obtain the infinitesimal deformation generated by virtue of a Nijenhuis operator. It is obtained that the sufficient and necessary condition for the equivalence of abelian extensions of Hom-δ-Jordan Lie supertriple systems.

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22

Mavambou, A. M., N. M. Moukala, and V. B. Nkou. "A NOTE ON NONDEGENERATE POISSON STRUCTURE." Advances in Mathematics: Scientific Journal 11, no. 11 (November 22, 2022): 1071–84. http://dx.doi.org/10.37418/amsj.11.11.8.

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The Schouten-Nijenhuis bracket on the module of K\"ahler differentials is introduced. We recover Lichnerowicz's notion of Poisson manifold by using the universal property of derivations. We prove using the Schouten-Nijenhuis bracket that a nondegenerate Poisson structure corresponds exactly to a symplectic structure. Finally, we explore the notion of Hamiltonian vector fields on a nondegenerate Poisson manifold in terms of derivations.

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23

Vanžura, Jiří. "Derivations on the Nijenhuis-Schouten bracket algebra." Czechoslovak Mathematical Journal 40, no. 4 (1990): 671–89. http://dx.doi.org/10.21136/cmj.1990.102420.

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24

Okubo, Susumu. "Poisson Brackets and Nijenhuis Tensor." Zeitschrift für Naturforschung A 52, no. 1-2 (February 1, 1997): 76–78. http://dx.doi.org/10.1515/zna-1997-1-220.

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Abstract Many integrable models satisfy the zero Nijenhuis tensor condition. Although its application for discrete systems is then straightforward, there exist some complications to utilize the condition for continuous infinite dimensional models. A brief sketch of how we deal with the problem is explained with an application to a continuous Toda lattice.

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25

Nunes da Costa, J. M., and Fani Petalidou. "Reduction of Jacobi–Nijenhuis manifolds." Journal of Geometry and Physics 41, no. 3 (March 2002): 181–95. http://dx.doi.org/10.1016/s0393-0440(01)00054-7.

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26

Migliorini, M., and A. Tomassini. "Nijenhuis tensors and lie algebras." Journal of Geometry and Physics 22, no. 3 (June 1997): 245–54. http://dx.doi.org/10.1016/s0393-0440(96)00033-2.

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27

Kosmann-Schwarzbach, Yvette. "Nijenhuis structures on Courant algebroids." Bulletin of the Brazilian Mathematical Society, New Series 42, no. 4 (December 2011): 625–49. http://dx.doi.org/10.1007/s00574-011-0032-5.

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28

Golovko, V. A. "Variational Schouten and Nijenhuis brackets." Russian Mathematical Surveys 63, no. 2 (April 30, 2008): 360–62. http://dx.doi.org/10.1070/rm2008v063n02abeh004522.

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29

Boualem, Hassan, and Robert Brouzet. "Semi-simple generalized Nijenhuis operators." Journal of Geometric Mechanics 4, no. 4 (2012): 385–95. http://dx.doi.org/10.3934/jgm.2012.4.385.

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30

Vaisman, Izu. "Reduction of Poisson-Nijenhuis manifolds." Journal of Geometry and Physics 19, no. 1 (May 1996): 90–98. http://dx.doi.org/10.1016/0393-0440(95)00024-0.

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31

Strohmayer, Henrik. "Operad profiles of Nijenhuis structures." Differential Geometry and its Applications 27, no. 6 (December 2009): 780–92. http://dx.doi.org/10.1016/j.difgeo.2009.03.014.

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32

Akpan, D. Zh. "Almost Differentially Nondegenerate Nijenhuis Operators." Russian Journal of Mathematical Physics 29, no. 4 (December 2022): 413–16. http://dx.doi.org/10.1134/s106192082204001x.

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33

Grabowski, Janusz. "Z-Graded Extensions of Poisson Brackets." Reviews in Mathematical Physics 09, no. 01 (January 1997): 1–27. http://dx.doi.org/10.1142/s0129055x97000026.

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A Z-graded Lie bracket { , }P on the exterior algebra Ω(M) of differential forms, which is an extension of the Poisson bracket of functions on a Poisson manifold (M,P), is found. This bracket is simultaneously graded skew-symmetric and satisfies the graded Jacobi identity. It is a kind of an 'integral' of the Koszul–Schouten bracket [ , ]P of differential forms in the sense that the exterior derivative is a bracket homomorphism: [dμ, dν]P=d{μ, ν}P. A naturally defined generalized Hamiltonian map is proved to be a homomorphism between { , }P and the Frölicher–Nijenhuis bracket of vector valued forms. Also relations of this graded Poisson bracket to the Schouten–Nijenhuis bracket and an extension of { , }P to a graded bracket on certain multivector fields, being an 'integral' of the Schouten–Nijenhuis bracket, are studied. All these constructions are generalized to tensor fields associated with an arbitrary Lie algebroid.

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34

Khan, Mohammad Nazrul Islam, Majid Ali Choudhary, and Sudhakar K. Chaubey. "Alternative Equations for Horizontal Lifts of the Metallic Structures from Manifold onto Tangent Bundle." Journal of Mathematics 2022 (April 26, 2022): 1–8. http://dx.doi.org/10.1155/2022/5037620.

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We explore “the horizontal lift” of the structure J satisfying J 2 − α J − β I = 0 and establish that it as a kind of metallic structure. An analysis of Nijenhuis tensor of metallic structure J H is presented, and a new tensor field J ˜ of 1,1 -type is introduced and demonstrated to be metallic structure. Some results on the Nijenhuis tensor and the Lie derivative of J ˜ in TM are proved and explicit examples are given. Moreover, the metallic structure J ˜ endowed with projection operators l ˜ and m ˜ in TM is studied.

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35

Khan, Mohammad Nazrul Islam, Majid Ali Choudhary, and Sudhakar K. Chaubey. "Alternative Equations for Horizontal Lifts of the Metallic Structures from Manifold onto Tangent Bundle." Journal of Mathematics 2022 (April 26, 2022): 1–8. http://dx.doi.org/10.1155/2022/5037620.

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Abstract:

We explore “the horizontal lift” of the structure J satisfying J 2 − α J − β I = 0 and establish that it as a kind of metallic structure. An analysis of Nijenhuis tensor of metallic structure J H is presented, and a new tensor field J ˜ of 1,1 -type is introduced and demonstrated to be metallic structure. Some results on the Nijenhuis tensor and the Lie derivative of J ˜ in TM are proved and explicit examples are given. Moreover, the metallic structure J ˜ endowed with projection operators l ˜ and m ˜ in TM is studied.

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36

Khan, Mohammad Nazrul Islam, Majid Ali Choudhary, and Sudhakar K. Chaubey. "Alternative Equations for Horizontal Lifts of the Metallic Structures from Manifold onto Tangent Bundle." Journal of Mathematics 2022 (April 26, 2022): 1–8. http://dx.doi.org/10.1155/2022/5037620.

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Abstract:

We explore “the horizontal lift” of the structure J satisfying J 2 − α J − β I = 0 and establish that it as a kind of metallic structure. An analysis of Nijenhuis tensor of metallic structure J H is presented, and a new tensor field J ˜ of 1,1 -type is introduced and demonstrated to be metallic structure. Some results on the Nijenhuis tensor and the Lie derivative of J ˜ in TM are proved and explicit examples are given. Moreover, the metallic structure J ˜ endowed with projection operators l ˜ and m ˜ in TM is studied.

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37

Das, Apurba, and Sourav Sen. "Nijenhuis operators on Hom-Lie algebras." Communications in Algebra 50, no. 3 (October 16, 2021): 1038–54. http://dx.doi.org/10.1080/00927872.2021.1977942.

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38

Wade, Aïssa. "Cosymplectic-Nijenhuis structures on Lie groupoids." Banach Center Publications 110 (2016): 295–307. http://dx.doi.org/10.4064/bc110-0-19.

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39

Kosmann‐Schwarzbach, Y., and F. Magri. "Lax–Nijenhuis operators for integrable systems." Journal of Mathematical Physics 37, no. 12 (December 1996): 6173–97. http://dx.doi.org/10.1063/1.531771.

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40

Liu, Jie-Feng, Yun-He Sheng, Yan-Qiu Zhou, and Cheng-Ming Bai. "Nijenhuis Operators on n -Lie Algebras." Communications in Theoretical Physics 65, no. 6 (June 1, 2016): 659–70. http://dx.doi.org/10.1088/0253-6102/65/6/659.

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41

Bao-Kang, Liu, and He Long-Guang. "Dirac-nijenhuis structures on lie bialgebroids." Reports on Mathematical Physics 55, no. 2 (April 2005): 179–98. http://dx.doi.org/10.1016/s0034-4877(05)00010-8.

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42

Bao-Kang, Liu, and He Long-Guang. "Some properties of Dirac-Nijenhuis manifolds." Reports on Mathematical Physics 58, no. 2 (October 2006): 165–94. http://dx.doi.org/10.1016/s0034-4877(06)80046-7.

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43

Grabowski, Janusz, and Paweł Urbański. "Lie algebroids and Poisson-Nijenhuis structures." Reports on Mathematical Physics 40, no. 2 (October 1997): 195–208. http://dx.doi.org/10.1016/s0034-4877(97)85916-2.

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44

Wade, Aı̈ssa. "A generalization of Poisson–Nijenhuis structures." Journal of Geometry and Physics 39, no. 3 (September 2001): 217–32. http://dx.doi.org/10.1016/s0393-0440(01)00015-8.

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45

Petalidou, Fani, and J. M. Nunes da Costa. "Local structure of Jacobi–Nijenhuis manifolds." Journal of Geometry and Physics 45, no. 3-4 (March 2003): 323–67. http://dx.doi.org/10.1016/s0393-0440(01)00074-2.

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46

MAGNANO, G., and F. MAGRI. "POISSON-NIJENHUIS STRUCTURES AND SATO HIERARCHY." Reviews in Mathematical Physics 03, no. 04 (December 1991): 403–66. http://dx.doi.org/10.1142/s0129055x91000151.

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We show that the direct sum of n copies of a Lie algebra is endowed with a sequence of affine Lie-Poisson brackets, which are pairwise compatible and define a multi-Hamiltonian structure; to this structure one can associate a recursion operator and a Kac-Moody algebra of Hamiltonian vector fields. If the initial Lie algebra is taken to be an associative algebra of differential operators, a suitable family of Hamiltonian vector fields reproduce either the n-th Gel'fand-Dikii hierarchy (for n finite) or Sato's hierarchy (for n = ∞). Within the same framework, it is also possible to recover a class of integro-differential hierarchies involving a finite number of fields, which generalize the Gel'fand-Dikii equations and are equivalent to Sato's hierarchy.

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47

Evans, Jonathan David. "The infimum of the Nijenhuis energy." Mathematical Research Letters 19, no. 2 (2012): 383–88. http://dx.doi.org/10.4310/mrl.2012.v19.n2.a10.

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48

Antunes, Paulo. "Poisson Quasi-Nijenhuis Structures with Background." Letters in Mathematical Physics 86, no. 1 (October 2008): 33–45. http://dx.doi.org/10.1007/s11005-008-0272-5.

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49

Bogoyavlenskij, Oleg I. "Algebraic identities for the Nijenhuis tensors." Differential Geometry and its Applications 24, no. 5 (September 2006): 447–57. http://dx.doi.org/10.1016/j.difgeo.2006.02.009.

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50

Abdujabborov, N. G., I. A. Karimjanov, and M. A. Kodirova. "Rota-type operators on 3-dimensional nilpotent associative algebras." Communications in Mathematics 29, no. 2 (June 1, 2021): 227–41. http://dx.doi.org/10.2478/cm-2021-0020.

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