ICI - CMA | Documentos por Auto-Depósito
URI permanente para esta coleção:
Navegar
Entradas recentes
- On a ternary octonion algebraPublication . Beites, Patrícia Damas ; Nicolás, Alejandro; Córdova Martínez, Alejandra SarinaFollowing a research direction proposed in an earlier work, the ternary octonion algebra O, which is a ternary composition algebra, is considered. By hand and applying computational linear algebra on matrices, 1-identities and 2-identities of O are established. From some of these identities, the non-conservativeness of O and of some of its binary reduced algebras, which are binary standard composition algebras of types II and III, is proved. Also from identities of O, using computational linear algebra based on the representation theory of the symmetric group, ternary enveloping algebras for ternary Maltsev algebras are constructed.
- A note on simple, 4-dimensional, ternary Filippov algebrasPublication . Beites, Patrícia Damas ; Nicolás, AlejandroProperties of simple, 4-dimensional, ternary Filippov algebras are presented. More concretely, 1-identities and 2-identities, conservativeness and some equations are studied.
- Geonardo numbersPublication . Moreira, Catarina; Beites, Patrícia DamasInspired by the term Gibonacci numbers, which was coined by A. T. Benjamin and J. J. Quinn as shorthand for generalized Fibonacci numbers, Geonardo numbers are considered. More concretely, for each a ∈ N0, the study of the sequence of generalized Leonardo numbers associated with a, introduced in an earlier work, is continued and new properties of these numbers are studied: parity; forms of Binet’s formula; growth of consecutive Geonardo numbers plus a ∈ N0; generating functions – ordinary, exponential, Poisson; identities – sum-binomial, Catalan, Cassini, d’Ocagne, Melham. In addition, some unknown equalities and inequalities related to Leonardo numbers are previously established.
- Short (SL2 × SL2)-structures on Lie algebrasPublication . Beites, Patrícia Damas ; Córdova Martínez, Alejandra Sarina; Cunha, Isabel; Elduque, AlbertoS-structures on Lie algebras, introduced by Vinberg, represent a broad generalization of the notion of gradings by abelian groups. Gradings by, not necessarily reduced, root systems provide many examples of natural S-structures. Here we deal with a situation not covered by these gradings: the short (SL2 × SL2)-structures, where the reductive group is the simplest semisimple but not simple reductive group. The algebraic objects that coordinatize these structures are the J -ternary algebras of Allison, endowed with a nontrivial idempotent.
- Transposed Poisson StructuresPublication . Beites, Patrícia Damas ; Ferreira, Bruno; Kaygorodov, IvanTo present a survey on known results from the theory of transposed Poisson algebras, as well as to establish new results on this subject, are the main aims of the present paper. Furthermore, a list of open questions for future research is given.
- On the Leonardo quaternions sequencePublication . Beites, Patrícia Damas ; Catarino, Paula Maria Machado CruzIn the present work, a new sequence of quaternions related to the Leonardo numbers – named the Leonardo quaternions sequence – is defined and studied. Binet’s formula and certain sum and binomial-sum identities, some of which derived from the mentioned formula, are established. Tagiuri-Vajda’s identity and, as consequences, Catalan’s identity, d’Ocagne’s identity and Cassini’s identity are presented. Furthermore, applying Catalan’s identity, and the connection between composition algebras and vector cross product algebras, Gelin-Cesàro’s identity is also stated and proved. Finally, the generating function, the exponential generating function and the Poisson generating function are deduced. In addition to the results on Leonardo quaternions, known results on Leonardo numbers and on Fibonacci quaternions are extended.
- Multiplication of closed balls in C^nPublication . Beites, Patrícia Damas ; Nicolás, Alejandro; Vitoria, JoseMotivated by circular complex interval arithmetic, some operations on closed balls in Cn are considered. Essentially, the properties of possible multiplications for closed balls in Cn, related either to the Hadamard product of vectors or to the 2-fold vector cross product when n ∈ {3, 7}, are studied. In addition, certain equations involving the defined multiplications are solved.
- The algebraic and geometric classification of transposed Poisson algebrasPublication . Beites, Patrícia Damas ; Fernández Ouaridi, Amir; Kaygorodov, IvanThe algebraic and geometric classification of all complex 3-dimensional transposed Poisson algebras is obtained. Also we discuss special 3-dimensional transposed Poisson algebras.
- Skew-symmetric matrices related to the vector cross product in C^7Publication . Beites, Patrícia Damas ; Nicolás, Alejandro; Vitoria, JoseSkew-symmetric matrices of order 7 defined through the 2-fold vector cross product in C7 , and other related matrices, are presented. More concretely, matrix properties, namely invertibility, nullspace, powers and index, are studied. As a consequence, results on vector cross product equations, vector cross product differential equations and vector cross product difference equations in C7 are established.
- Uma fórmula de tipo Binet para os números de GeonardoPublication . Moreira, Catarina; França, Pedro; Beites, Patrícia DamasO termo "números de Geonardo" ‒ forma abreviada de designar uma generalização dos números de Leonardo criada por P. D. Beites - é inspirado na obra intitulada Proofs that Reallly Count, na qual A. T. Benjamin e J. J. Quinn definem os números de Gibonacci ‒ forma abreviada de designar os números de Fibonacci por eles generalizados.