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Dr. habil. Stepan DoupliiPen/scientific name Steven Duplij Center for Information Technology University of Münster Röntgenstr. 7-13 (Rm. 115 in №9) 48149 Münster T: +49 251 83-31530 F: +49 251 83-31555 Previous homepage (with other activities): Steven Duplij's homepage Ancient unupdated version : Steven Duplij's U.S. homepage |
Research Areas
Quantum computing, mathematics, theoretical physics.
On Web
CV
PDF in GermanPDF in English, extended, clickable links to articles
Degrees
2002 The academic status of Senior Research Fellow is given by Higher Certifying Commission, Kiev, Ukraine1999 Habilitation Thesis: "Semigroup Methods in Supersymmetric Theories of Elementary Particles", Bogolyubov Institute of Theoretical Physics, Kiev, Ukraine, Doctor Habilitatus in Theoretical Physics (Doctor of Science in Physics and Mathematics)
1983 Ph.D. Thesis: "Theoretical Investigation of Hard Processes in QCD";
1978-1982 Post Graduate Course in Theoretical Physics, Kharkov State University; PhD (Candidate of Science in Physics and Mathematics); adviser M.P. Rekalo
Education
1994-1995 Special German Language Course, Goethe Institute, Mannheim, Germany; Distinguished diploma1974-1978 Department of Theoretical Physics, Kharkov State University; The Distinguished Diploma in Theoretical Nuclear Physics - M.Sc.
1973-1976 Special English Language Course, Kharkov State University; The Distinguished Diploma
1973-1974 Department of Theoretical Radiophysics, Kharkov State University
Positions (work experience 47 years)
2018-present Senior Staff Researcher, Center for Information Technology, Universität Münster, Münster, Germany2016-2017 Lecturer in Mathematics, University of Applied Sciences, Bochum, Germany
2014-2016 Scientific Researcher, Mathematisches Institut, Universität Münster, Münster, Germany
2000-2014 Lead Senior Staff Researcher, Nuclear Physics Laboratory, Kharkov National University, Kharkov, Ukraine
1983-1992 Staff Researcher, Nuclear Physics Laboratory, Kharkov State University, Kharkov, Ukraine
1978-1982 Half-time Researcher, Radiophysics Laboratory, Kharkov State University, Kharkov, Ukraine
1977-1978 Researcher, Kharkov Institute of Physics and Technology, Kharkov, Ukraine
Grants
2011-2012 Fulbright Scholar Program, Rutgers University, Piscataway, USA (host: G.A. Goldin) Fulbright S.D. Profile2007 American Physical Society Travel Grant, Johns Hopkins University, USA (host: J. Bagger)
1994-1997 Alexander von Humboldt Fellowship, University of Kaiserslautern, Kaiserslautern, Germany (initial host: W. Rϋhl, follow up hosts: J. Cuntz, F. Müller-Hoissen, M. Zirnbauer) AvH S.D. Profile
Scientific visits
S. Adler, H. Arodz, M.A. Aukhadiev, J. Bagger, M. Bianchi, L. Bonora, B. Broda, C. Burdik, R. Casalbuoni, S. Catto, Jiejing Cheng, M. Ciric, A. Comtet, J. Cuntz, M. Dabrowski, C. Delizia, A. Douglas, B. Dragovich, W. Dudek, G. Esposito, P. Etingof, A.M. Gal'mak, D.V. Gal'tsov, G.A. Goldin, S.A. Grigoryan, H. Grosse, D. Grumiller, Qiang Guo, U. Günther, L. Kauffman, R. Kotiuga, M.I. Krivoruchenko, J. Kupsch, M. Lapidus, M.I. Levchuk, Fang Li, Kang Li, E. Lomon, J. Lukierski, L. Lusanna, W. Marcinek, A. Martsinkovsky, M. Mulase, F. Müller-Hoissen, Chi-Keung Ng, W. Von Oertzen, J. Okninski, N. Poncin, A.Ya. Radyno, M. Schlichenmaier, A. Schwarz, M. Shifman, W. Siegel, G.L. Stavraki, C. Ringel, V. Rittenberg, W. Rühl, J. Stasheff, X. Tata, M. Tonin, P. Urbanski, A. Vilenkin, K. Wali, J. Wess, G. Wolschin, S. Woronowicz, R. Wulkenhaar, Yun-Long Xu, Zheng Yu, C. Zachos, M. Zirnbauer, M. ZnojilScientific results and innovative ideas
PDF (with direct links from ideas to articles)HTML (as a separate page with new ideas linked to articles)
Even- and odd-reduced supermatrices are introduced and considered on a par, being complementary in terms of the newely obtained Berezinian addition formula, and are unified into a kind of "sandwich" semigroup. A special subset of odd-reduced supermatrices represent higher order rectangular bands for which new generalized "fine" Green's relations and egg-box diagrams are constructed. One-parameter semigroups of idempotent odd-reduced supermatrices and corresponding superoperator semigroups are introduced and studied by the new semigroup × semigroup method. The linear idempotent superoperators and exponential superoperators are mutually dual in some sense, and the first gives rise to an additional noninvertible non-exponential solutions to the initial Cauchy problem. A novel permanent-determinant symmetry is found for even complex superplane. It is shown that the corresponding counterparts (per analogs) of the cross ratio, distance and harmonic set are invariant under the introduced per mapping, a special noninvertible subset of the fractional linear transformation. The per analogs of the Laguerre formula for distance and Schwarzian derivative are presented.
An additional superextension of complex structure is uncovered, which is noninvertible and can correspond to another (odd) superanalog of Riemann surfaces and to the counterpart of superconformal-like transformations which twist the parity of tangent space and their nonlinear realization, which together with the ordinary ones form the superconformal semigroup having special unusual properties. A unique formula connecting berezinian, permanent and determinant is obtained. From a physical viewpoint, the above conceptions can lead to semistatistics, being von Neumann regular analog of the ordinary statistics.
The arity invariance principle, a manifest expression of algebraic structure in terms of operations independent of their arities, is claimed. The relations of the von Neumann regular semigroups and the Artin braid group were found, and a higher arity generalization gave the polyadic-binary correspondence, which allowed the definition of the following new structures: higher braid groups, higher degree analogs of Coxeter group and Artin braid group. The following were also uncovered: unusual polyadic rings and fields (which can, remarkably, be zeroless and nonunital) having addition and multiplication of different arities, polyadic integer numbers and p-adic integers, polyadic convolution products having multiplication and comultiplication of different arities and their corresponding polyadic Hopf algebra and n-ary R-matrix, polyadic multistar adjoints and polyadic operator C*-algebras and Cuntz algebras. The polyadic analogs of the Lander–Parkin–Selfridge conjecture and Fermat's Last Theorem were formulated.
It is proposed that mediality as a principle is more natural, unique and universal than commutativity in generalizing the latter to n-ary algebras (in the binary case commutativity directly follows from mediality). This is called the commutativity-to-mediality ansatz, which is applied to obtain almost medial n-ary graded algebras, a new kind of tensor categories, polyadic nonunital "groupal" categories with "quertors" (analogs of querelements in n-ary groups), "medialed" tensor categories and querfunctors. A principally new mechanism of additional "continuous noncommutativity", governed by a special "membership deformation" of commutativity for algebras with the underlying set as obscure/fuzzy set, is introduced. Using the membership deformation factor together with the ordinary graded commutation factor, the almost commutative graded (n-ary) algebras and Lie algebras with double commutativity are obtained, and their projective representations are studied.
As a first step towards a the polyadic algebraic K-theory, the Grothendieck construction of the completion group for a monoid is generalized to the case, where both are of different, higher arities. As opposed to the binary case, an identity is not necessary for the initial m-ary semigroup to obtain a class n-ary group, which in turn need not contain an identity.
A new (infinite) class of division algebras, the hyperpolyadic algebras, which correspond to the (only 4) binary division algebras R, C, H, O (reals, complex numbers, quaternions, octonions) are defined. A polyadic analog of the Cayley-Dickson construction is proposed, and a novel iterative process gives "half-quaternions" and "half-octonions". New polyadic algebras with higher brackets which have (as opposed to n-ary Lie algebras) different arity from the initial n-ary algebra multiplication, are introduced. The sigma matrices and the Pauli group are generalized to higher arities. Using them, a toy model of one-dimensional supersymmetric quantum mechanics was constructed, as a first example of polyadic supersymmetry, which is specially extended in a way different from the new multigraded SQM previously proposed.
Scientific publications
PDF (1985-2024) mathematical physics, quantum computing and DNA structure (161 items)
PDF (1980-1985) radiophysics and nuclear physics, particle physics and quantum chromodynamics (31 items)
HTML (1985-2008) with links to articles (105 items)
In total: 192 publications, among them 9 books and 183 articles.
In addition: 130 entries (table in PDF) in Concise Encyclopedia of Supersymmetry.
Coeditors
J. Bagger, W. Siegel, M.L. Walker, J. Wess, V. Zima
Coauthors
V.P. Akulov, A.Yu. Berezhnoy, A. Borowiec, A.J. Bruce, N. Chashchin, V.V. Chitov, M. Chursin, A. Frydryszak, O.M. Getmanetz, E. Di Grezia, W. Dudek, D.R. Duplij, N.V. Duplii, V.P. Duplij, G. Esposito, G.A. Goldin, Y. Hong, V.V. Kalashnikov, O.I. Kotulska, A.T. Kotvytskiy, G.Ch. Kurinnoj, S.V. Landar, F. Li, Y.G. Mashkarov, W. Marcinek, E.A. Maslov, N.M. Pelykhaty, V.M. Puzh, M.P. Rekalo, M.A. Rukavitsyn, A. Sadovnikov, Z.S. Sagan, S. Sinel'shchikov, I.I. Shapoval, V.M. Shtelen, D.V. Soroka, V.A. Soroka, S.A. Steshenko, R. Vogl, M.L. Walker, W. Werner, I.I. Zalyubovsky
Recent 2018-2024
2024
S. Duplij, Polyadic sigma matrices, J. Math. Phys. 65 (2024), 083509 , listed in Editor's Picks, preprint arXiv:2403.19361 (PDF) [math.GT], 19 pages, 2024.S. Duplij, Hyperpolyadic structures, Mathematics 12 (2024), 2378, 29 pages.
S. Duplij, Polyadic supersymmerty, preprint arXiv:2406.02188 [hep-th], 14 pages, 2024.
V.P. Duplij, N.V. Duplii, S. Duplij, DNA walk diagram in Triander and jsTriander applications, Plant Phys. Genet. (Fiziol. rast. genet.) 56 (2024), no. 4, 353-361.
2023
BooksS. Duplij, R. Vogl, Innovative Quantum Computing, IOP Publishing (Bristol-London) 2023, 178 pages.
Articles
S. Duplij, Hyperpolyadic structures, preprint arXiv:2312.01366 [math.RA], 29 pages, 2023.
S. Duplij, R. Vogl, Polyander visualization of quantum walks, preprint arXiv:2311.00409 [quant-ph], 12 pages, 2023.
S. Duplij, R. Vogl, On superqubits, preprint arXiv:2310.09635 [quant-ph], 14 pages, 2023.
2022
BooksS. Duplij, Polyadic Algebraic Structures, IOP Publishing (Bristol-London) 2022, 461 pages.
Selected Topics in Gravity, Field Theory and Quantum Mechanics, S. Duplij and M.L. Walker, Editors, MDPI Books, Basel, 2022, 348 pages. https://www.mdpi.com/books/book/6455.
Articles
S. Duplij, Polyadic analogs of direct product, Universe 8 (2022), 230.
S. Duplij, Polyadic rings of p-adic integers, Symmetry 14 (2022), 2591.
S. Duplij, Polyadization of algebraic structures, Symmetry 14 (2022), 1782.
M.L. Walker and S. Duplij, Gauge gravity vacuum in constraintless Clairaut-type formalism, Universe 8 (2022), 176.
S. Duplij and W. Werner, Extensions of special 3-fields, preprint arXiv:2212.08606 [math.RA], 22 pages, 2022.
2021
ArticlesS. Duplij and W. Werner, Structure of unital 3-fields, Math. Semesterber. 68 (2021), 27–53.
S. Duplij, Polyadic Hopf algebras and quantum groups, East European J. Phys. 2 (2021), 5–50 (arXiv:1811.02712).
S. Duplij, Higher braid groups and regular semigroups from polyadic-binary correspondence, Mathematics 9 (2021), 972.
S. Duplij, Graded medial n-ary algebras and polyadic tensor categories, Symmetry 13 (2021), 1038.
M.L. Walker and S. Duplij, Gauge gravity vacuum in constraintless Clairaut-type formalism, preprint arXiv: 2106.07723, 23 pages, 2021.
S. Duplij and R. Vogl, Polyadic braid operators and higher braiding gates, Universe 7 (2021), 301.
S. Duplij and R. Vogl, Obscure qubits and membership amplitudes, in Topics on Quantum Information Science, S. Curilef and A. R. Plastino, eds., IntechOpen, London, 2021, 20 pp.
S. Duplij, Membership deformation of commutativity and obscure n-ary algebras, J. Math. Physics, Analysis, Geometry 17 (2021), 441–462 (arXiv:2006.07865).
A.J. Bruce and S. Duplij, Double-graded quantum superplane, Rep. Math. Phys. 86 (2020), 383–400 (arXiv:1910.12950).
A.J. Bruce and S. Duplij, Double-graded supersymmetric quantum mechanics, J. Math. Phys. 61 (2020), 063503, 13 ( arXiv:1904.06975).
2019
ArticlesS. Duplij, Supergravity Was Discovered by D.V. Volkov and V.A. Soroka in 1973, Wasn’t it? East European J. Phys. (2019), 3, 81-82 (arXiv:1910.03259).
S. Duplij, Arity shape of polyadic algebraic structures, J. Math. Physics, Analysis, Geometry 15 (2019), 3–56 (arXiv:1703.10132).
A.J. Bruce and S. Duplij, Double-graded quantum superplane, Univ. Luxembourg, preprint arXiv:1910.12950, 2019.
2018
BooksS. Duplij, Exotic Algebraic and Geometric Structures in Theoretical Physics, Nova Publishers, New York, 2018, 410 pp.
Articles
G.A. Goldin, V.M. Shtelen, and S. Duplij, Conformal symmetry transformations and nonlinear Maxwell equations, in Mathematical Structures and Applications, T. Diagana and B. Toni, eds., Springer, Berlin, 2018, pp. 211–224.
S. Duplij, Polyadic Hopf algebras and quantum groups, preprint arXiv:math.RA/1811.02712, 57 pages, 2018.