Algebraic Structures and Applications: SPAS 2017, Västerås and Stockholm, Sweden, October 4-6 (Springer Proceedings in Mathematics & Statistics (317))

This book explores the latest advances in algebraic structures and applications, and focuses on mathematical concepts, methods, structures, problems, algorithms and computational methods important in the natural sciences, engineering and modern technologies. In particular, it features mathematical methods and models of non-commutative and non-associative algebras, hom-algebra structures, generalizations of differential calculus, quantum deformations of algebras, Lie algebras and their generalizations, semi-groups and groups, constructive algebra, matrix analysis and its interplay with topology, knot theory, dynamical systems, functional analysis, stochastic processes, perturbation analysis of Markov chains, and applications in network analysis, financial mathematics and engineering mathematics. The book addresses both theory and applications, which are illustrated with a wealth of ideas, proofs and examples to help readers understand the material and develop new mathematical methods and concepts of their own. The high-quality chapters share a wealth of new methods and results, review cutting-edge research and discuss open problems and directions for future research. Taken together, they offer a source of inspiration for a broad range of researchers and research students whose work involves algebraic structures and their applications, probability theory and mathematical statistics, applied mathematics, engineering mathematics and related areas. Front Matter ....Pages i-xxx Weil Algebra, 3-Lie Algebra and B.R.S. Algebra (Viktor Abramov)....Pages 1-12 Algebras with Ternary Composition Law Combining \(\mathrm {Z_2}\) and \(\mathrm {Z_3}\) Gradings (Viktor Abramov, Richard Kerner, Olga Liivapuu)....Pages 13-45 Ternary Lie Superalgebras and Nambu-Hamilton Equation in Superspace (Viktor Abramov, Priit Lätt)....Pages 47-80 Generalized Derivations of n-BiHom-Lie Algebras (Amine Ben Abdeljelil, Mohamed Elhamdadi, Ivan Kaygorodov, Abdenacer Makhlouf)....Pages 81-97 On n-ary Generalization of BiHom-Lie Algebras and BiHom-Associative Algebras (Abdennour Kitouni, Sergei Silvestrov, Abdenacer Makhlouf)....Pages 99-126 On Solvability and Nilpotency for n-Hom-Lie Algebras and \((n+1)\)-Hom-Lie Algebras Induced by n-Hom-Lie Algebras (Abdennour Kitouni, Abdenacer Makhlouf, Sergei Silvestrov)....Pages 127-157 Multiplicative n-Hom-Lie Color Algebras (Ibrahima Bakayoko, Sergei Silvestrov)....Pages 159-187 On Classification of Filiform Hom-Lie Algebras (Abdenacer Makhlouf, Mourad Mehidi)....Pages 189-221 Classification of Low-Dimensional Hom-Lie Algebras (Elvice Ongong’a, Johan Richter, Sergei Silvestrov)....Pages 223-256 Enveloping Algebras of Certain Types of Color Hom-Lie Algebras (Abdoreza Armakan, Sergei Silvestrov)....Pages 257-284 A Review on Hom-Gerstenhaber Algebras and Hom-Lie Algebroids (Satyendra Kumar Mishra, Sergei Silvestrov)....Pages 285-315 Strong Hom-Associativity (Lars Hellström)....Pages 317-337 On Hom-Yetter-Drinfeld Category (Tianshui Ma, Sergei Silvestrov, Huihui Zheng)....Pages 339-358 On the Classification of f-Quandles (Indu Rasika Churchill, Mohamed Elhamdadi, Nicolas Van Kempen)....Pages 359-369 Noncommutatively Graded Algebras (Patrik Nystedt)....Pages 371-383 Differential Calculi on Associative Algebras and Integrable Systems (Aristophanes Dimakis, Folkert Müller-Hoissen)....Pages 385-410 The Jacobian Conjecture\(_{2n}\) Implies the Dixmier Problem\(_n\) (Vladimir V. Bavula)....Pages 411-426 Commutants in Crossed Product Algebras for Piecewise Constant Functions on the Real Line (Alex Behakanira Tumwesigye, Johan Richter, Sergei Silvestrov)....Pages 427-444 Ore Extensions of Function Algebras (Alex Behakanira Tumwesigye, Johan Richter, Sergei Silvestrov)....Pages 445-467 Centralizers in PBW Extensions (Alex Behakanira Tumwesigye, Johan Richter, Sergei Silvestrov)....Pages 469-490 Reordering, Centralizers and Centers in an Algebra with Three Generators and Lie Type Relations (John Musonda, Sten Kaijser, Sergei Silvestrov)....Pages 491-508 Reordering in Noncommutative Algebras Associated with Iterated Function Systems (John Musonda, Johan Richter, Sergei Silvestrov)....Pages 509-552 Twisted Difference Operator Representations of Deformed Lie Type Commutation Relations (John Musonda, Johan Richter, Sergei Silvestrov)....Pages 553-573 Torsion-Type q-Deformed Heisenberg Algebra and Its Lie Polynomials (Rafael Reno Cantuba, Sergei Silvestrov)....Pages 575-592 Lie Polynomial Characterization Problems (Rafael Reno Cantuba, Sergei Silvestrov)....Pages 593-601 Relations Between the Fractional Operators in q-Calculus (Sergei Silvestrov, Predrag M. Rajković, Sladjana D. Marinković, Miomir S. Stanković)....Pages 603-624 On the Exponential and Trigonometric \(q,\omega \)-Special Functions (Thomas Ernst)....Pages 625-651 Isomorphism Theorems for Basic Constructive Algebraic Structures with Special Emphasize On Constructive Semigroups with Apartness—An Overview (Melanija Mitrović, Sergei Silvestrov)....Pages 653-686 Semilatice Decompositions of Semigroups. Hereditariness and Periodicity—An Overview (Melanija Mitrović, Sergei Silvestrov)....Pages 687-721 Common Fixed Point for Integral Type Contractive Mappings in Multiplicative Metric Spaces (Talat Nazir, Sergei Silvestrov)....Pages 723-741 Cyclic Contractions and Common Fixed Point Results of Integral Type Contractions in Multiplicative Metric Spaces (Talat Nazir, Sergei Silvestrov)....Pages 743-759 Extreme Points of the Vandermonde Determinant on the Sphere and Some Limits Involving the Generalized Vandermonde Determinant (Karl Lundengård, Jonas Österberg, Sergei Silvestrov)....Pages 761-789 Extreme Points of the Vandermonde Determinant on Surfaces Implicitly Determined by a Univariate Polynomial (Asaph Keikara Muhumuza, Karl Lundengård, Jonas Österberg, Sergei Silvestrov, John Magero Mango, Godwin Kakuba)....Pages 791-818 Optimization of the Wishart Joint Eigenvalue Probability Density Distribution Based on the Vandermonde Determinant (Asaph Keikara Muhumuza, Karl Lundengård, Jonas Österberg, Sergei Silvestrov, John Magero Mango, Godwin Kakuba)....Pages 819-838 An Algebraic Method for Pricing Financial Instruments on Post-crisis Market (Anatoliy Malyarenko, Hossein Nohrouzian, Sergei Silvestrov)....Pages 839-856 Advanced Monte Carlo Pricing of European Options in a Market Model with Two Stochastic Volatilities (Betuel Canhanga, Anatoliy Malyarenko, Jean-Paul Murara, Ying Ni, Sergei Silvestrov)....Pages 857-874 Lie Symmetry Analysis on Pricing Weather Derivatives by Partial Differential Equations (Clarinda Nhangumbe, Ebrahim Fredericks, Betuel Canhanga)....Pages 875-901 Perturbation Analysis for Stationary Distributions of Markov Chains with Damping Component (Dmitrii Silvestrov, Sergei Silvestrov, Benard Abola, Pitos Seleka Biganda, Christopher Engström, John Magero Mango et al.)....Pages 903-933 Uniqueness of p-Adic Gibbs Measures for p-Adic \(\lambda \)-Ising Model on Cayley Tree of Arbitrary Order (Mutlay Dogan)....Pages 935-944 On Pade Approximants Series Solutions of MHD Flow Equations with Heat and Mass Transfer Due to a Point Sink (Imran Chandarki, Brijbhan Singh)....Pages 945-959 Back Matter ....Pages 961-968