Publications (A. Makhlouf)
1.Ternary Distributive Structures and Quandles,
Kyungpook Mathematical Journal, (2016) (with M. Elhamdadi and M. Green).
2.On (n+1)-Hom-Lie Algebras Induced by n-Hom-Lie Algebras,
Georgian Mathematical Journal (2016) (with A. Kitouni and S. Silvestrov)
3.BiHom-associative algebras, BiHom-Lie algebras and BiHom-bialgebras,
Symmetry, Integrability and Geometry : Methods and Applications SIGMA 11 (2015),
086, 34 pages (with G. Graziani, C. Menini, F. Panaite).
4.Hom-L-R-smash products, Hom-diagonal crossed products and the Drinfeld double of a
Hom-Hopf algebra.
Journal of Algebra, 441, (2015). (with F. Panaite)
5.Non-Commutative ternary Nambu-Poisson algebras and ternary Hom-Nambu-Poisson algebras,
J Generalized Lie Theory Appl 9 : 221. doi :10.4172/1736-4337.1000221 (2015),
(with H. Amri)
6.Brackets with (tau;sigma)-derivations and (p; q)-deformations of Witt and Virasoro algebras,
Forum Math. 2015 (with O. Elchinger, K. Lundengard, S. Silvestrov).
7.Twisting operators, twisted tensor products and smash products for Hom-associative algebras,
Glasgow Math. J. : doi :10.1017/S0017089515000294 (2015). (with F. Panaite).
8.Hom-Alternative, Hom-Malcev and Hom-Jordan superalgebras,
Bulletin of the Malaysian Mathematical Sciences Society 2015. (with K. Abdaoui et F. Ammar)
9.Constructions and Cohomology of Hom-Lie Colour Algebras,
Communications in Algebra (2015). (with K. Abdaoui et F. Ammar)
10.Kaplansky’s Type Constructions for Weak bialgebras and Weak Hopf algebras,
J Generalized Lie Theory Appl S1 : 008. doi :10.4172/1736-4337.S1-008 (2015), (with Z. Chebel).
11.On Classification of finite dimensional superbialgebras and Hopf superalgebras,
Symmetry, Integrability and Geometry : Methods and Applications SIGMA 10 (2014),
001, 24 (with S. Aissaoui)
12.Yetter-Drinfeld modules for Hom-bialgebras,
Journal of Mathematical Physics 55, 013501 (2014) ; doi : 10.1063/1.4858875 (2014) (with F. Panaite)
13.Hom-Lie algebras with symmetric invariant nondegenerate bilinear forms,
Journal of Geometry and Physics, 76, pp 38–60 (2014) (with S. Benayadi)
14.Drinfeld twisting elements on Hom-bialgebras,
Journal of Physics : Conference Series 532 (2014) 012017 (with B. Torrecillas)
15.Universal Algebra Applied to Hom-Associative Algebras, and More,
in Algebra, Geometry and Mathematical Physics,
Springer Proceedings in Mathematics & Statistics, 85 2014, (151–192) (with L. Hellström, S. Silvestrov)
16.Constructions of Quadratic n-ary Hom-Nambu algebras,
in Algebra, Geometry and Mathematical Physics,
Springer Proceedings in Mathematics & Statistics, 85 2014, (193–224) (with F. Ammar, S. Mabrouk)
17.Rota-Baxter Hom-Lie-admissible algebras,
Communications in algebra, 42 n° 3 (2013) (with D. Yau).
18. Hom-quasi-bialgebras,
Contemporary Math. Vol. 585 (2013) (Eds. N. Andruskievich, J. Cuadra and B. Torrecillas)
(with M. Elhamdadi).
19.Cohomology of Hom-Lie superalgebras and q-deformed Witt superalgebra,
Czechoslovak Mathematical Journal, Vol. 63, No. 3, (2013), (with F. Ammar, N. Saadaoui)
20.Hom-dendriform Algebras and Rota-Baxter Hom-algebras,
Proc. Int. Conf., in Nankai Series in Pure, Applied Mathematics and Theoretical Physics,
(Eds. C. Bai, L. Guo and J-L.Loday),
Vol. 9 (World Scientific, Singapore, 2012), 147–171.
21. Twisting Poisson algebras, coPoisson algebras and Quantization,
Travaux Mathématiques, Volume 20 (2012), 83–119, (with M. Bordemann, O. Elchinger)
22.Graphic Illustration of the Transmission Resonances for the DKP Particles,
Applications and Applied Mathematics : An International Journal, Vol. 8, Issue 2, 733–740 ( 2013), (with Boutabia-Cheraitia)
23.Second Cohomology of q-deformed Witt superalgebras,
Journal of Mathematical Physics 54, 063507 (2013) ; http ://dx.doi.org/10.1063/1.4807717 (2013), (with F. Ammar et N. Saadaoui).
24. Index of filiform and quasi-filiform Lie algebras,
Filomat 27 (2013), no. 3, 467–483. (with H. Adimi).
25.Objets algébriques de base, cohomologie et application aux déformations,
dans Gravitation quantique : Théorie et Applications, Hermann Edition, Travaux en cours 79 , ISBN 978 2 7056 8049 7, Paris (2013) Chap. 7, pp 291–334.
26.Construction of n-Lie algebras and n-ary Hom-Nambu-Lie algebras,
Journ. Math. Phys. 52, 123502 (2011) ; doi : 10.1063/1.3653197 (with J. Arnlind et S. Silvestrov).
27. Relativistic Oscillators in a Noncommutative Space : a Path Integral Approach,
Zeitschrift fuer Naturforschung (2011) DOI : 10.5560/ZNA.2011-0060
(with H. Benzair, M. Merad, T. Boudjedaa)
28. Deformations of Hom-Alternative and Hom-Malcev Algebras,
Group, Algebra and Geometries, (2012) arXiv :1006.2499 ( with M. Elhamdadi).
29. Representations and Cohomology of n-ary multiplicative Hom-Nambu-Lie algebras,
Journal of Geometry and Physics (2011), DOI 10.1016/j.geomphys.2011.04.022
(with F. Ammar, S. Mabrouk).
30. Cohomology and Deformations of Hom-algebras,
Journal of Lie Theory 21 No. 4, (2011) 813–836 , (with F. Ammar et Z. Ejbehi).
31. Cohomology and Deformations of Alternative algebras,
Journal of Generalized Lie Theory and Applications, Vol. 5 (2011), Article ID G110105,
doi :10.4303/jglta/G110105 (2011) ( with M. Elhamdadi).
32. Hom-alternative algebras and Hom-Jordan algebras,
International Eletronic Journal of Algebra, Volume 8 (2010) 177-190.
33. Hom-Lie Superalgebras and Hom-Lie admissible Superalgebras,
Journal of Algebra, Vol. 324, Issue 7, 1513–1528 (2010) , (with F. Ammar)
34. Ternary q-Virasoro-Witt Hom-Nambu-Lie algebras,
Journal of Physics A : Mathematical and Theoretical, 43 (2010) 265204.
(with F. Ammar et S. Silvestrov)
35. Hom-algebras and Hom-coalgebras,
Journal of Algebra and Its Applications Vol. 9 (4), 553–589 (2010), (with S. Silvestrov).
36. Computing Indexes of Lie algebras algebras,
Proceedings of the Estonian Academy of Science 59, 4, 265‹271, (2010), (with H. Adimi).
37. Notes on 1-parameter formal deformations of Hom-associative and Hom-Lie algebras,
Forum Mathematicum, vol. 22 (4) (2010), 715–739., (with S. Silvestrov).
38. Ternary Hom-Nambu-Lie algebras induced by Hom-Lie algebras,
Journal of Mathematical Physics, 51, 043515 (2010) ; doi :10.1063/1.3359004 (2010)
(with J. Arnlind et S. Silvestrov)
39. Coactions on Hochschild homology of Hopf-Galois extensions and their coinvariants,
Journal of Pure and Applied Algebra, Vol. 214, Issue 9, pp 1654-1677 (2010), (with D. Stefan)
40. Formality and free algebras,
Oberwolfach report Volume 7, Issue 3, 2010, pp. 2503‹2560 DOI : 10.4171/OWR/2010/43
Deformation Methods in Mathematics and Physics (Editors : A. Fialowski, J. M. Frõhlich
and M. Schlichenmaier) (with O. Elchinger, M. Bordemann and S. Gutt)
41. Paradigm of Nonassociative Hom-algebras and Hom-superalgebras,
Proceedings of Jordan Structures in Algebra and Analysis Meeting, Eds : J. Carmona Tapia,
A. Morales Campoy, A. M. Peralta Pereira, M. I. Ramírez Álvarez,
ISBN : 978-84-92849-51-2 Publishing house : Circulo Rojo, (2010) ( 145–177)
42. Generalization of n-ary Nambu algebras and beyond,
Journal of Mathematical Physics 50, no. 8, 083501, (2009) (with H. Ataguema et S. Silvestrov)
43. Notes on cohomologies of ternary algebras of associative type,
Journal of Generalized Lie Theory and Applications 3 no. 3, pp 157–174, (2009)
(with H. Ataguema)
44.Bialgebra structures of 2-associative algebras,
Arabian Journal of Science and Engineering, Volume 33, Number 2C, 137–151 (2008)
(with K. Dekkar)
45.Hom-algebra structures,
Journal of Generalized Lie Theory and Applications, vol. 2 (2) , 51–64 (2008),
(with S. Silvestrov)
46.Hom-Lie admissible Hom-Coalgebras and Hom-Hopf Algebras,
In "Generalized Lie Theory in Mathematics, Physics and Beyond",
Editors V. Abramov, E. Paal, S. Silvestrov and A. Stolin, Springer (2008), (with S. Silvestrov)
47.Formality and Deformations of Universal Enveloping Algebras,
International Journal of Theoretical Physics, Volume 47, Issue 2, pp. 311-332 (2008),
(with M. Bordemann)
48.Algèbres de Hopf et renormalisation en théorie des champs quantiques,
Dans "Théorie quantique des champs : Méthodes et applications", Collection Travaux en
cours Physique-Mathématiques, Editions Hermann (2007), (56 pages).
49.Deformations of ternary algebras,
Journal of Generalized Lie Theory and Applications, vol. 1, pp 41-45 (2007),
(with H. Ataguema)
50.A comparison of deformations and geometric study of varieties of associative algebras,
International Journal of Mathematics and Mathematical Science Volume 2007 (2007),
Article ID 18915, (24 pages).
51.Sur les structures algébriques issues de la physique : groupe quantique, algèbre de Hopf
et structure de Poisson,
Actes des journées scientifiques algéro-Françaises en Mathématiques et physique théorique.
Publication de l’UHA, (2006)
52.Sur les bialgèbres et algèbres de Hopf faibles en dimensions <4,
Actes des journées scientifiques algéro-Françaises en Mathématiques et physique théorique.
Publication de l’UHA, (2006) (avec Chebel)
53.Classification et déformation d’algèbres ternaires,
Actes des journées scientifiques algéro-Françaises en Mathématiques et physique théorique.
Publication de l’UHA, (2006) (avec Ataguema)
54.Déformation par quantification et rigidité des algèbres enveloppantes,
Journal of Algebra, vol. 285, pp 623-648 (2005) ( with M. Bordemann et T. Petit)
55.Degeneration, rigidity and irreducible components of Hopf algebras,
Algebra Colloquium, Vol. 12 n 2 pp 241-254, (2005)
56.Schwinger action principle via linear quantum canonical transformations,
European physical Journal C, 20, pp 1-10 (2005) (with M. Bouloudenine et T. Boudjedaa)
57.Standard subalgebras of semisimple Lie algebras and computer-aided for enumeration
Annales Mathématiques Blaise Pascal 10, pp 315-326 (2003)
(with Y. Hakimjanov et B. Es Saadi)
58. Algèbres associatives et calcul formel,
Theoretical Computer Science, vol. 187, pp 123-145, (1997)
59.Classification of rigid associative algebras in low dimensions
Collection travaux en cours Hermann (ed. M. Goze), pp 5-22, (1996), (with M. Goze)
60.Sur les algèbres associatives caractéristiquement nilpotentes
Communications in algebra, 22 (8), pp 2961-2967, (1994), (with M. Goze et Y. Hakimjanov)
61.Irreducible components of nilpotent associative algebras,
Revista Matematica de la Universidad complutense de Madrid, vol 6 n_1, pp 27-40, (1993)
62.2-nilpotent rigid associative algebras
Rendiconti del seminario de Cagliari, vol. 62 n_1, pp 9-14, (1992), (with M. Goze)
63.On rigid complex associative algebras
Communications in algebra, 18 (12), pp 4031-4046, (1990), (with M. Goze).
Publications internes / Internal Publications
64.Exploring algebraic geometry with computer algebra system and applications
Preprints in mathematical sciences, Lund University, Centre for Mathematical Sciences,
Centrum scientiarum mathematicarum, (2006 :11) LUTFMA-5074-2006 (112 pages).
65.Sur les structures algébriques issues de la physique : groupe quantique, algèbre de Hopf et structure de Poisson,
Actes des journées scientifiques algéro-Françaises en Mathématiques et physique théorique.
Publication de l’UHA, (2006)
66.Sur les bialgèbres et algèbres de Hopf faibles en dimensions <4,
Actes des journées scientifiques algéro-Françaises en Mathématiques et physique théorique.
Publication de l’UHA, (2006) (with Chebel)
67.Classification et déformation d’algèbres ternaires,
Actes des journées scientifiques algéro-Françaises en Mathématiques et physique théorique.
Publication de l’UHA, (2006) (with Ataguema)
68.Deformation theories of algebraic structures
Publication interne, (2004) (47 pages).
69.Application du calcul formel dans les calculs cohomologiques de structures algébriques
Actes des Journées nationales de Calcul Formel de Luminy , (2003).
70.Sur les invariants matriciels des algèbres associatives
Actes du colloque Matrix and applications, Seville, (1997).
71.Eléments génériques non standard en algèbres
Actes du colloque trajectorien, IRMA Strasbourg (1995) (with M. Goze).
72.Rigid associative algebras and quivers
Actes du colloque de Wuppertal , (1989).
73.Deformation by quantization of enveloping algebras,
Oberwolfach report (2006). (with Bordemann et Petit).
74.Explorer la géométrie algébrique à l’aide d’un système de calcul formel
Publication de l’Université de Cagliari (2001).
75.Sur les algèbres associatives rigides
Publication IRMA Strasbourg, 391/P-218, (1989) (71 pages).
76.La cohomologie de Chevalley d’une algèbre de Lie
Publication IRMA Strasbourg, 357/P-198, (1987) (With M. Goze).
77. Application des méthodes infinitésimales aux algèbres associatives complexes
Publication de l’Université de Seville (1992) (40 pages).
Publications en didactique / Didactics
78. Sur l’approche en termes d’ordre de grandeur absolu de l’enseignement de l’Analyse
Actes du colloque de Mulhouse (Mai 2002),
Publication de l’IREM de Strasbourg (2004) (avec le groupe GrOG)
79. Analyse en termes d’ordres de grandeur : de l’intuition au concept
Publication de l’IREM de Strasbourg (2002) (avec le groupe GrOG) (88 pages)
ISBN 2-911446-17-8.
80. Introduction à la dérivation et au calcul integral en termes d’ordres de grandeur.
Actes des journées nationales APMEP de Nice 2000 (avec R. Lutz)
81. Le Quizz de l’an 2000, (avec le groupe IREM calcul formel)
jeu mathématique sur ordinateur consultable sur le site
www.math.univ-mulhouse.fr/quizz2000/
82. L’Analyse au lycée en termes d’ordres de grandeur : un essai pratique
Bulletin vert de l’APMEP Num. 428. p. 397-401, (2000) (avec E. Meyer)
83. Faire des maths avec un logiciel de calcul formel
Brochure de l’IREM de Strasbourg, (1996).
(avec le groupe calcul formel Mulhouse), (169 pages) ISBN 2-911446-04-6
84. La proportionalité,
Brochure de l’IREM de Strasbourg, (1995). (avec le groupe collège Mulhouse)
85. Mathématiques assistée par ordinateur : un complément et une nécessité.
Prépublication.
86. L’enseignement de l’Analyse en l’an 2000,
Bulletin vert de l’APMEP Num. 411. p. 558-571, (1997) (avec R. Lutz et E. Meyer)
87. L’enseignement de l’analyse en termes d’ordres de grandeur : nécessité et fondement.
Revue REPERE IREM, (1996), (avec Lutz et Meyer)
88. CDRom d’Analyse (avec le groupe IREM calcul formel).
www.math.univ-mulhouse.fr/analyse/
89. Cyber-exposition sur l’Univers de Pi (avec l’équipe d’algèbre) :
www.math.univ-mulhouse.fr/~irem/Pi/