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- Arithmetic for closed ballsPublication . Beites, P. D.; Nicolás, A. P.; Vitoria, JoseInspired by circular complex interval arithmetic, an arithmetic for closed balls in Rn is pursued. In this sense, the properties of certain operations on closed balls in Rn, some of which related either to the Hadamard product of vectors or to the 2-fold vector cross product when n ∈ {3, 7}, are studied. In particular, known results for operations on closed balls in C, which can be identified with R2, are extended to closed balls in Rn.
- A Note on Standard Composition Algebras of Types II and IIIPublication . Beites, P. D.; Nicolás, AlejandroSome identities satis ed by certain standard composition algebras, of types II and III, are studied and become candidates for the characterization of the mentioned types.[...]
- Vector cross product differential and difference equations in R-3 and in R-7Publication . Beites, P. D.; Nicolás, A. P.; Saraiva, Paulo; Vitoria, JoseThrough a matrix approach of the 2-fold vector cross product in R^3 and in R^7, some vector cross product di erential and di erence equations are studied. Either the classical theory or convenient Drazin inverses, of elements belonging to the class of index 1 matrices, are applied.
- On skew-symmetric matrices related to the vector cross product in R^7Publication . Beites, P. D.; Nicolás, Alejandro; Vitoria, JoseA study of real skew-symmetric matrices of orders 7 and 8, de ned through the vector cross product in R7, is presented. More concretely, results on matrix properties, eigenvalues, (generalized) inverses and rotation matrices are established.
- 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.
- 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.
- 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.
- 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.