Research & Professional Achievements
Research & Professional Achievements
Research Interests:
Hopf algebras and Quantum Groups, Lie (super)algebras, θ-colored G-graded Lie algebras and Universal Enveloping Algebras, Paraparticle Algebras, Parastatistics,
Mathematics and Physics of (parastatistical) many-body quantum systems including the modeling and study of radiation-matter interactions in such systems
Mathematical Physics, Representation Theory, Quasitriangularity, Braided Monoidal Categories, Abelian Categories, Derived Categories and Derived Functors, Triangulated Categories
Gravitational Models with Branes and Computation of Corrections with respect to Newtonian Gravity, Generalized Spheroidal Wave Equations (GSWE) and Heun equations (Construction and Convergence of Power Series Solutions), 3-term recurrences (TTR) with rational coefficients and construction of minimal solutions (arithmetically and analytically).
■Links in databases indexing/reviewing my published research:
Google Scholar, Mathreviews/ MathScinet, Zentralblatt MATH, INSPIRE-HEP, SCOPUS, ISI Web of Science
■ Link at the arXiv with my published work: arXiv.org/Kanakoglou
■ Online samples of my research can be found at: MathOverflow/kanakoglou
■Referee/Reviewer: Math Rev (MathSciNet), Zentralblatt MATH, SIGMA, British Journal of Mathematics and Computer Science (BJMCS)
N. Barbosa-Cendejas, A. Herrera-Aguilar, K.Kanakoglou, U.Nucamendi, I.Quiros, “Mass hierarchy, mass gap and corrections to Newton’s law on thick branes with Poincaré symmetry”, General Relativity and Gravitation, v.46,1,1631, 2014
K.Kanakoglou, “Gradings, Braidings, Representations, Paraparticles: Some open problems”, Axioms, v.1, 1, 2012, p.74-98
N.Barbosa-Cendejas, A.Herrera-Aguilar, K.Kanakoglou, J.E.Paschalis, “Nonlinear hidden symmetries in General Relativity and String theory: a matrix generalization of the Ernst potentials”, Electronic Journal of Theoretical Physics, v.8, Zacatecas Proc. II, 2011, p.17-29
K.Kanakoglou, A.Herrera-Aguilar, “Ladder operators, Fock-spaces, irreducibility and group gradings for the Relative Parabose Set algebra”, International Journal of Algebra, v.5, 9, 2011, p.413-428
K.Kanakoglou, A. Herrera-Aguilar, “Graded Fock--like representations for a system of algebraically interacting paraparticles”, Journal of Physics: Conf. Ser., v.287, 012037, 2011
K.Kanakoglou, C.Daskaloyannis, A.Herrera-Aguilar, “Super-Hopf realizations of Lie Superalgebras: Braided Paraparticle extensions of the Jordan-Schwinger map”, AIP Conference Proceedings, v.1256, p. 193-200, 2010
K.Kanakoglou, C.Daskaloyannis, “Variants of bosonization in Parabosonic algebra: the Hopf and super-Hopf structures in Parabosonic algebra”, Journal of Physics A: Mathematical and Theoretical, v.41, 105203, 2008
K.Kanakoglou, C.Daskaloyannis, “Bosonization and Parastatistics: an example and an alternative approach”, at: GENERALIZED LIE THEORY IN MATHEMATICS, PHYSICS AND BEYOND, p.207-218, eds.: S.Silvestrov et al, SPRINGER, 2008
K.Kanakoglou, C.Daskaloyannis, “A braided look at Green ansatz for parabosons”, Journal of Mathematical Physics, v.48, 113516, 2007
K.Kanakoglou, C.Daskaloyannis, “Graded structure and Hopf structures in Parabosonic algebra: an alternative approach to bosonization”, at: NEW TECHNIQUES IN HOPF ALGEBRAS AND GRADED RING THEORY, p.105-116, eds.: S.Caenpeel, et al, Royal Flemish Academy of Belgium, 2007, arXiv:0706.2825[math-ph]
A.Herrera-Aguilar, K.Kanakoglou, J.E.Paschalis, “Towards the establishment of non-linear hidden symmetries in the Skyrme model”, AIP Conference Proceedings, v.857, p.194-201, 2006
C.Daskaloyannis, K.Kanakoglou, I.Tsohantzis, “Hopf algebraic structure of the Parabosonic and Parafermionic algebras and paraparticle generalizations of the Jordan-Schwinger map”, Journal of Mathematical Physics, v.41, 2, p.652-660, 2000
D.Bonatsos, C.Daskaloyannis, K.Kanakoglou, “Parafermionic and generalizad Parafermionic algebras”, Proceedings of the International Conference on QUANTUM GROUPS, DEFORMATIONS AND CONTRACTIONS, Instabul, TURKEY, 1999, arXiv:hep-th/9909002v1
D.Bonatsos, C.Daskaloyannis, K.Kanakoglou, G.Petsos, “Parafermions and generalized Parafermions in Physical systems”, Proceedings of the 16th International Workshop on Nuclear Theory, Rila, BULGARIA, 1997
K.Kanakoglou, A. Herrera-Aguilar, “Towards applications of graded Paraparticle algebras”, HNPS:Proceedings of the 19th Hellenic Nuclear Physics Society Symposium, HNPS2010, vol. 18 (2010), p.181-186, Thessaloniki, 28-29 May 2010
K.Kanakoglou, C.Daskaloyannis, “Parabosonic and Parafermionic algebras: Graded structure and Hopf structures”, Proceedings of the 6th Panhellenic Conference of Algebra and Number Theory (PCANT), editors: Th. Theohari-Apostolidi,Ch. Charalampous, Thessaloniki 2006, arXiv:hep-th/0701077v1
A.Herrera-Aguilar, K.Kanakoglou, J.E.Paschalis, “On Hidden Symmetries of the Skyrme model”, HNPS:ADVANCES IN NUCLEAR PHYSICS, NUCLEAR ASTROPHYSICS, HEAVY IONS AND RELATED AREAS: Proceedings of the 15th Panhellenic Symposium of the Hellenic Nuclear Physics Society, editors: G.A.Lalazisis, Ch.C.Moustakidis, HNPS2005, vol. 14 (2005), p. 179-184, Thessaloniki, 2005
D.Bonatsos, C.Daskaloyannis, K.Kanakoglou, I.Tsohantzis, “Applications of Parafermionic and Parabosonic algebras in Nuclear Physics”, HNPS:Proceedings of the 11th Panhellenic Symposium of the Hellenic Nuclear Physics Society, Thessaloniki, 2001
C.Daskaloyannis, D.Bonatsos, K.Kanakoglou, “Parafermionic mapping of the two-color delta model of interacting quarks”, HNPS:ADVANCES IN NUCLEAR PHYSICS, Proceedings of the 10th Panhellenic Symposium of the Hellenic Nuclear Physics Society, editors: p.Demetriou, N.Vodinas, HNPS1999, vol. 10 (1999), p.256-261, Athens, 1999,
K.Kanakoglou, “The notion of abstract manifold: a pedagogical approach”, Lecture notes, arXiv:1204.2191v1[math-ph], for a postgraduate course on Differential geometry at IFM, UMSNH