Algebra Without Borders - Classical and Constructive Nonassociative Algebraic Structures: Foundations and Applications

ISBN-13: 9783031393334 / Angielski

Mahouton Norbert Hounkonnou; Melanija Mitrovic; Mujahid Abbas

Spis treści

Quandles, knots, quandle rings and graphs (Elhamdadi).- New splittings of operations of Poisson algebras and transposed Poisson algebras and related algebraic structures (Bai).- Some varieties of loops (Bol-Moufang and non-Bol-Moufang types) (Sòlárìn).- The ����3-graded extension of the Poincaré algebra (Kerner).- Ternary Leibniz color algebras and beyond (Bakayoko).- (Hom-)(co)associative ternary (co)algebras and infinitesimal ternary (hom-)bialgebras (Hounkonnou).- Elduque-Myung type mutations of Hom-algebras (Silvestrov).- (Hom-) ���� -generalizedWitt algebras (Hounkonnou).- Some algebraic properties of representations of polynomial covariance commutation relations (Silvestrov).- Applications of Quasigroups in Cryptography and Coding Theory (Trpcheska).- Generalized quadratic quasigroup functional equations (Krapež).- A Primer on Noncommutative Classical Dynamics on Velocity Phase Space and Souriau Formalism (Guha).

O autorze

Mahouton Norbert Hounkonnou is a Full Professor at the Catholic University of Abomey-Calavi, Benin. He holds a PhD from the University of Louvain, Belgium. His works deal with noncommutative and nonlinear mathematics, including differential equations, operator theory, coherent states, quantization techniques, orthogonal polynomials, special functions, graph theory, nonassociative algebras, nonlinear integrable systems, noncommutative field theories, and geometric methods in physics and complexity.

Melanija Mitrović is a Full Professor at the University of Niš, Serbia, having received her PhD degree at the same university. She has held visiting professor positions at Malardaren University, Sweden; Bar-Ilan University, Israel; TU Wien, Austria; UTAD and University of Minho, Portugal; and Politecnico di Milano, Italy. She develops interdisciplinary research investigating applications of algebraic structures to problems in engineering space. Her lines of research are in basic classical and constructive algebraic structures.

Mujahid Abbas is a Full Professor at the Government College University, Pakistan. He holds a PhD from the National College for Business Administration and Economics, Pakistan. His research is focused on fixed-point theory and its applications, topological vector spaces and nonlinear operators, best approximations, fuzzy logic, and convex optimization theory.

Madad Khan is an Associate Professor at the COMSATS University Islamabad–Abbottabad Campus, Pakistan. He holds a PhD from Quaid-i-Azam University, Islamabad, Pakistan, and did post-doctorate studies at the University of Birmingham, UK, and the University of Chicago, USA. His research interests lie in biomathematics, fuzzy mathematics, computational mathematics, group theory, and generalizations.

Blurb

This book gathers invited, peer-reviewed works presented at the 2021 edition of the Classical and Constructive Nonassociative Algebraic Structures: Foundations and Applications—CaCNAS: FA 2021, virtually held from June 30 to July 2, 2021, in dedication to the memory of Professor Nebojša Stevanović (1962-2009). The papers cover new trends in the field, focusing on the growing development of applications in other disciplines. These aspects interplay in the same cadence, promoting interactions between theory and applications, and between nonassociative algebraic structures and various fields in pure and applied mathematics.

In this volume, the reader will find novel studies on topics such as left almost algebras, logical algebras, groupoids and their generalizations, algebraic geometry and its relations with quiver algebras, enumerative combinatorics, representation theory, fuzzy logic and foundation theory, fuzzy algebraic structures, group amalgams, computer-aided development and transformation of the theory of nonassociative algebraic structures, and applications within natural sciences and engineering.

Researchers and graduate students in algebraic structures and their applications can hugely benefit from this book, which can also interest any researcher exploring multi-disciplinarity and complexity in the scientific realm.