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Dive into the research topics where Jesús Laliena is active.

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Featured researches published by Jesús Laliena.


Communications in Algebra | 2000

On the lie structure of the skew elements of a prime superalgebra with superinvolution

Carlos Gómez-Ambrosi; Jesús Laliena; Ivan Shestakov

We investigate the Lie structure of the Lie superalgebra K of skew elements of a prime associative superalgebra A with superinvolution. It is proved that if A is not a central order in a Clifford superalgebra of dimension at most 16 over the center then any Lie ideal of K or [K,K] contains[J ∩K,K] for some nonzero ideal J of A or is contained in the even part of the center of A.


arXiv: Rings and Algebras | 2007

THE KAC JORDAN SUPERALGEBRA : AUTOMORPHISMS AND MAXIMAL SUBALGEBRAS

Alberto Elduque; Jesús Laliena; Sara Sacristán

In this note the group of automorphisms of the Kac Jordan superalgebra is described, and used to classify the maximal subalgebras.


Communications in Algebra | 2009

On Certain Semiprime Associative Superalgebras

Jesús Laliena; Sara Sacristán

In this note we emphasise the relationship between the structure of an associative superalgebra with superinvolution and the structure of the Lie substructure of skewsymmetric elements. More explicitly, we show that if A is a semiprime associative superalgebra with superinvolution and K is the Lie superalgebra of skewsymmetric elements satisfying [K 2, K 2] = 0, then A is a subdirect product of orders in simple superalgebras each at most 4-dimensional over its center.


Linear & Multilinear Algebra | 2013

Superalgebras with superinvolution whose symmetric or skewsymmetric elements are regular

Jesús Laliena; Roberto Rizzo

We study semiprime superalgebras with superinvolution whose symmetric elements are not zero divisors, and semiprime superalgebras with superinvolution, with nonzero odd part, whose skewsymmetric elements are not zero divisors. We prove that, in both cases, such superalgebras are a domain or the subdirect sum of a domain and its opposite.


Journal of Algebra and Its Applications | 2014

On some Montgomery's results on algebras with involution in superalgebras

Jesús Laliena; Roberto Rizzo

We study semiprime superalgebras with superinvolution whose symmetric or skewsymmetric elements are assumed to be regular or nilpotent, and superalgebras in which xx* = 0 implies x*x = 0.


Archive | 1994

Lattice Isomorphisms of Jordan Algebras over Arbitrary Fields

Jesús Laliena

We study Jordan algebras M whose lattice of subalgebras is isomorphic to the lattice of subalgebras of a Jordan matrix algebra, J = H(D n , J A ), where D is either a quadratic extension field (if n ≥ 2), a central division quaternion algebra (if n ≥ 3) or a central division Cayley-Dickson algebra (if n = 3). We prove that M is also a Jordan matrix algebra of the same kind as J.


Journal of Algebra | 2004

Maximal subalgebras of associative superalgebras

Alberto Elduque; Jesús Laliena; Sara Sacristán


Journal of Pure and Applied Algebra | 2008

Maximal subalgebras of Jordan superalgebras

Alberto Elduque; Jesús Laliena; Sara Sacristán


Journal of Algebra | 2007

Lie structure in semiprime superalgebras with superinvolution

Jesús Laliena; Sara Sacristán


Journal of Algebra | 2010

Regularity conditions on skew and symmetric elements in superalgebras with superinvolution

Jesús Laliena; Sara Sacristán

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Ivan Shestakov

University of São Paulo

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