Non-Associative Algebras and Related Topics

ISBN-13: 9783031327063 / Angielski / Twarda / 2023

Opis

This proceedings volume presents a selection of peer-reviewed contributions from the Second Non-Associative Algebras and Related Topics (NAART II) conference, which was held at the University of Coimbra, Portugal, from July 18–22, 2022. The conference was held in honor of mathematician Alberto Elduque, who has made significant contributions to the study of non-associative structures such as Lie, Jordan, and Leibniz algebras. 

The papers in this volume are organized into four parts: Lie algebras, superalgebras, and groups; Leibniz algebras; associative and Jordan algebras; and other non-associative structures. They cover a variety of topics, including classification problems, special maps (automorphisms, derivations, etc.), constructions that relate different structures, and representation theory.

One of the unique features of NAART is that it is open to all topics related to non-associative algebras, including octonion algebras, composite algebras, Banach algebras, connections with geometry, applications in coding theory, combinatorial problems, and more. This diversity allows researchers from a range of fields to find the conference subjects interesting and discover connections with their own areas, even if they are not traditionally considered non-associative algebraists. 

Since its inception in 2011, NAART has been committed to fostering cross-disciplinary connections in the study of non-associative structures.

Spis treści

Part 1: Lie Algebras, Superalgebras and Groups.- 1.Local derivations of classical simple Lie algebras (S. Ayupov, K. Kudaybergenov).- 2. Examples and patterns on quadratic Lie algebras (P. Benito and J. Roldán-López).- 3. Reductive homogeneous spaces of the compact Lie group G2 (C. Draper and F. J. Palomo).- 4. On certain algebraic structures associated with Lie (super)algebras(N. Kamiya).- 5. Schreier’s type formulae and two scales for growth of Lie algebras and groups (V. Petrogradsky).- Part 2: Leibniz Algebras.- 6. Universal central extensions of compatible Leibniz algebras (J.M.C Mirás, M. Ladra).- 7. On some properties of generalized Lie-derivations of Leibniz algebras (J.M.C Mirás, N.P. Rego).- 8. Biderivations of low-dimensional Leibniz algebras (M. Mancini).- 9. Poisson structure on the invariants of pairs of matrices (R. Turdibaev).- Part 3. Associative and Jordan Algebras and Related Structures.- 10. Automorphisms, derivations and gradings of the split quartic Cayley algebra (V. Blasco and A. Daza-García).- 11. On a Theorem of Brauer-Cartan-Hua type in superalgebras (J. Laliena).- 12. Growth functions of Jordan algebras (C. Martínez and E. Zelmanov).- 13. The image of polynomials in one variable on the algebra of 3 × 3 upper triangular matrices (T.C. de Mello and D.Rodrigues).- Part 4: Other Nonassociative Structures.- 14. Simultaneous orthogonalization of inner products over arbitrary fields (Y. Cabrera, C. Gil, D. Martín and C. Martín).- 15. Invariant theory of free bicommutative algebras (V. Drensky).- 16. An approach to the classification of finite semifields by quantum computing (J.M.H. Cáceres, I.F. Rúa).- 17.On ideals and derived and central descending series of n-ary Hom-algebras (A. Kitouni, S. Mboya, E. Ongong’a, S. Silvestrov).- 18. Okubo algebras with isotropic norm (A. Elduque).

O autorze

Helena Albuquerque is a Professor at the Center for Mathematics at the University of Coimbra, Portugal. She holds a PhD in Mathematics from the same university (1993). Her research focuses on non-associative algebras.

Jose Brox is currently a postdoc researcher at the University of Valladolid, Spain. He holds a PhD in Mathematics from the University of Málaga (2015). His previous research at the Center for Mathematics of the University of Coimbra focused on combinatorial algebra and non-associative structures.

Consuelo Martínez is a Professor at the University of Oviedo, Spain, where she coordinated the Graduate Program in Mathematics. She holds a PhD from the University of Zaragoza, Spain (1980). In 2018, Dr. Martínez was awarded the Real Sociedad Matemática de España Medal for her research contributions. In the same year, she also received the "Julio Peláez" Prize for Pioneer Women in Sciences awarded by the Tatiana Pérez de Gusmán Foundation for her achievements in mathematics. Her research activities focus on non-associative algebras and superalgebras and their interconnections with cryptography and coding theory.

Paulo Saraiva is a Professor at the Faculty of Economics of the University of Coimbra, Portugal. He holds a PhD in Mathematical Economics and Econometric Models from the same university (2004). His research, as a member of the Algebra and Combinatorics Group of the Center for Mathematics of the University of Coimbra, focuses on non-associative algebras.