Estudo Geralhttps://estudogeral.sib.uc.ptThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Tue, 28 Jan 2020 10:18:54 GMT2020-01-28T10:18:54Z5091Quasialgebra Structure of the Octonionshttp://hdl.handle.net/10316/4660Title: Quasialgebra Structure of the Octonions
Authors: Albuquerque, Helena; Majid, Shahn
Abstract: We show that the octonions are a twisting of the group algebra of 2 × 2 × 2 in the quasitensor category of representations of a quasi-Hopf algebra associated to a group 3-cocycle. In particular, we show that they are quasialgebras associative up to a 3-cocycle isomorphism. We show that one may make general constructions for quasialgebras exactly along the lines of the associative theory, including quasilinear algebra, representation theory, and an automorphism quasi-Hopf algebra. We study the algebraic properties of quasialgebras of the type which includes the octonions. Further examples include the higher 2n-onion Cayley algebras and examples associated to Hadamard matrices.
Fri, 01 Jan 1999 00:00:00 GMThttp://hdl.handle.net/10316/46601999-01-01T00:00:00ZOdd-quadratic Lie superalgebrashttp://hdl.handle.net/10316/11303Title: Odd-quadratic Lie superalgebras
Authors: Albuquerque, Helena; Barreiro, Elisabete; Benayadi, Saïd
Abstract: An odd-quadratic Lie superalgebra is a Lie superalgebra with a nondegenerate
supersymmetric odd invariant bilinear form. In this paper we give examples
and present some properties of odd-quadratic Lie superalgebras, introduce the
notions of double extension and generalized double extension of odd-quadratic Lie
superalgebras and give an inductive classi cation of odd-quadratic Lie superalgebras
such that the even part is a reductive Lie algebra
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/10316/113032007-01-01T00:00:00ZQuadratic Lie superalgebras with reductive even parthttp://hdl.handle.net/10316/11304Title: Quadratic Lie superalgebras with reductive even part
Authors: Albuquerque, Helena; Barreiro, Elisabete; Benayadi, Saïd
Abstract: The aim of this paper is to exibit some non trivial examples of quadratic
Lie superalgebras such that the even part is a reductive Lie algebra and the action
of the even part on the odd part is not completely reducible and to give an inductive
classi cation of this class of quadratic Lie superalgebras. The notion of generalized
double extension of quadratic Lie superalgebras proposed by I. Bajo, S. Benayadi
and M. Bordemann [1] has a crucial importance in this work. In particular we will
improve some results of [4], in the sense that we will not demand that the action of
the even part on the odd part is completely reducible, which naturally makes the
proofs of our results more diffcult.
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/10316/113042007-01-01T00:00:00ZThe structure of Leibniz superalgebras admitting a multiplicative basishttp://hdl.handle.net/10316/43773Title: The structure of Leibniz superalgebras admitting a multiplicative basis
Authors: Albuquerque, Helena; Barreiro, Elisabete; Calderón Martín, Antonio J.; Sánchez Delgado, José María
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10316/437732016-01-01T00:00:00ZAkivis superalgebras and specialityhttp://hdl.handle.net/10316/11270Title: Akivis superalgebras and speciality
Authors: Albuquerque, Helena; Santana, Ana Paula
Abstract: In this paper we define Akivis superalgebra and study enveloping superalgebras
for this class of algebras, proving an analogous of the PBW Theorem.
Lie and Malcev superalgebras are examples of Akivis superalgebras. For these
particular superalgebras, we describe the connection between the classical enveloping
superalgebras and the corresponding generalized concept defined in this work.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/10316/112702008-01-01T00:00:00ZMultiplicative invariant lattices in obtained by twisting of group algebras and some explicit characterizationshttp://hdl.handle.net/10316/4596Title: Multiplicative invariant lattices in obtained by twisting of group algebras and some explicit characterizations
Authors: Albuquerque, Helena; Kraußhar, Rolf Sören
Abstract: Let G be a finite group and be its group algebra defined over . If we define in G a 2-cochain F, then we can consider the algebra which is obtained from deforming the product, x.Fy=F(x,y)xy, [for all]x,y[set membership, variant]G. Examples of algebras are Clifford algebras and Cayley algebras like octonions. In this paper we consider generalizations of lattices with complex multiplication in the context of these twisted group algebras. We explain how these induce the natural algebraic structure to endow any arbitrary finite-dimensional lattice whose real components stem from any finite algebraic field extension over with a multiplicative closed structure. Furthermore, we develop some fully explicit characterizations in terms of generalized trace and norm functions.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/10316/45962008-01-01T00:00:00ZContribuições para a teoria das superálgebras de Malcev. Coimbra, ed. aut., 1993.http://hdl.handle.net/10316/1982Title: Contribuições para a teoria das superálgebras de Malcev. Coimbra, ed. aut., 1993.
Authors: Albuquerque, Helena Maria Mamede
Fri, 01 Jan 1993 00:00:00 GMThttp://hdl.handle.net/10316/19821993-01-01T00:00:00ZHomogeneous Symmetric Antiassociative Quasialgebrashttp://hdl.handle.net/10316/43825Title: Homogeneous Symmetric Antiassociative Quasialgebras
Authors: Albuquerque, Helena; Barreiro, Elisabete; Benayadi, Saïd
Abstract: Our main purpose is to provide for homogeneous (even or odd) symmetric antiassociative quasialgebras a structure theory analogous to that for homogeneous symmetric associative superalgebras given in [5] and to present an inductive description of these classes of algebras.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10316/438252014-01-01T00:00:00ZQuadratic Malcev superalgebrashttp://hdl.handle.net/10316/4640Title: Quadratic Malcev superalgebras
Authors: Albuquerque, Helena; Benayadi, Saïd
Abstract: A quadratic Malcev superalgebra is a Malcev superalgebra with a non-degenerate supersymmetric even invariant bilinear form B; B is called an invariant scalar product on M. In this paper, we obtain the inductive classifications of quadratic Malcev algebras and of Malcev superalgebras such that is a reductive Malcev algebra and the action of the on is completely reducible.
Thu, 01 Jan 2004 00:00:00 GMThttp://hdl.handle.net/10316/46402004-01-01T00:00:00Z