Jesus Laliena - Academia.edu (original) (raw)
Papers by Jesus Laliena
Acta Mathematica Hungarica, 1992
Springer proceedings in mathematics & statistics, 2023
arXiv (Cornell University), Jan 12, 2007
arXiv (Cornell University), Jun 1, 2006
The maximal subalgebras of the finite dimensional simple special Jordan superalgebras over an alg... more The maximal subalgebras of the finite dimensional simple special Jordan superalgebras over an algebraically closed field of characteristic 0 are studied. This is a continuation of a previous paper by the same authors about maximal subalgebras of simple associative superalgebras, which is instrumental here.
arXiv (Cornell University), Jul 11, 2013
In this paper we investigate the Lie structure of the derived Lie superalgebra [K, K], with K the... more In this paper we investigate the Lie structure of the derived Lie superalgebra [K, K], with K the set of skew elements of a semiprime associative superalgebra A with superinvolution. We show that if U is a Lie ideal of [K, K], then either there exists an ideal J of A such that the Lie ideal [J ∩ K, K] is nonzero and contained in U , or A is a subdirect sum of A ′ , A ′′ , where the image of U in A ′ is central, and A ′′ is a subdirect product of orders in simple superalgebras, each at most 16-dimensional over its center.
arXiv (Cornell University), Apr 11, 2016
In this paper we introduce an equivalence between the category of the tnilpotent quadratic Lie al... more In this paper we introduce an equivalence between the category of the tnilpotent quadratic Lie algebras with d generators and the category of some symmetric invariant bilinear forms over the t-nilpotent free Lie algebra with d generators. Taking into account this equivalence, t-nilpotent quadratic Lie algebras with d generators are classified (up to isometric isomorphisms, and over any field of characteristic zero), in the following cases: d = 2 and t ≤ 5, d = 3 and t ≤ 3.
Linear Algebra and its Applications, 2017
In this paper we introduce an equivalence between the category of the tnilpotent quadratic Lie al... more In this paper we introduce an equivalence between the category of the tnilpotent quadratic Lie algebras with d generators and the category of some symmetric invariant bilinear forms over the t-nilpotent free Lie algebra with d generators. Taking into account this equivalence, t-nilpotent quadratic Lie algebras with d generators are classified (up to isometric isomorphisms, and over any field of characteristic zero), in the following cases: d = 2 and t ≤ 5, d = 3 and t ≤ 3.
Journal of Pure and Applied Algebra, 2008
In this paper some results on the Lie structure of prime superalgebras are discussed. We prove th... more In this paper some results on the Lie structure of prime superalgebras are discussed. We prove that, with the exception of some special cases, for a prime superalgebra, A, over a ring of scalars Φ with 1/2∈Φ, if L is a Lie ideal of A and W is a subalgebra of A such that [W, L]⊆ W, then either L⊆ Z or W⊆ Z. Likewise, if V is a submodule of A and [V, L]⊆ V, then either V⊆ Z or L⊆ Z or there exists an ideal of A, M, such that 0= [M,A]⊆ V. This work extends to prime superalgebras some results of I. N. Herstein, C. Lanski and S. Montgomery on prime algebras.
Proceedings of the American Mathematical Society, 2007
Proceedings of the American Mathematical Society, 2007
Communications in Algebra, Oct 8, 2009
J. M. Osborn described the simple algebras in which every nonzero symmetric element is invertible... more J. M. Osborn described the simple algebras in which every nonzero symmetric element is invertible, and semisimple algebras in which every symmetric element is either nilpotent or invertible. We give some analog theorems in superalgebras and results related with them.
A large number of algebraic structures, among which the associative and the Jordan algebras deser... more A large number of algebraic structures, among which the associative and the Jordan algebras deserve special mention, are closely related to the Lie algebras and to some interesting geometries. These relationships explain certain exceptional behaviors in Algebra and Geometry, which are nothing but manifestations of the same phenomena. In this note we analyze part of the research made during the last years by the research group of Algebra of the University of La Rioja. This research focuses on the study of non associative structures related to Lie algebras.
Acta Mathematica Hungarica, 1992
Springer proceedings in mathematics & statistics, 2023
arXiv (Cornell University), Jan 12, 2007
arXiv (Cornell University), Jun 1, 2006
The maximal subalgebras of the finite dimensional simple special Jordan superalgebras over an alg... more The maximal subalgebras of the finite dimensional simple special Jordan superalgebras over an algebraically closed field of characteristic 0 are studied. This is a continuation of a previous paper by the same authors about maximal subalgebras of simple associative superalgebras, which is instrumental here.
arXiv (Cornell University), Jul 11, 2013
In this paper we investigate the Lie structure of the derived Lie superalgebra [K, K], with K the... more In this paper we investigate the Lie structure of the derived Lie superalgebra [K, K], with K the set of skew elements of a semiprime associative superalgebra A with superinvolution. We show that if U is a Lie ideal of [K, K], then either there exists an ideal J of A such that the Lie ideal [J ∩ K, K] is nonzero and contained in U , or A is a subdirect sum of A ′ , A ′′ , where the image of U in A ′ is central, and A ′′ is a subdirect product of orders in simple superalgebras, each at most 16-dimensional over its center.
arXiv (Cornell University), Apr 11, 2016
In this paper we introduce an equivalence between the category of the tnilpotent quadratic Lie al... more In this paper we introduce an equivalence between the category of the tnilpotent quadratic Lie algebras with d generators and the category of some symmetric invariant bilinear forms over the t-nilpotent free Lie algebra with d generators. Taking into account this equivalence, t-nilpotent quadratic Lie algebras with d generators are classified (up to isometric isomorphisms, and over any field of characteristic zero), in the following cases: d = 2 and t ≤ 5, d = 3 and t ≤ 3.
Linear Algebra and its Applications, 2017
In this paper we introduce an equivalence between the category of the tnilpotent quadratic Lie al... more In this paper we introduce an equivalence between the category of the tnilpotent quadratic Lie algebras with d generators and the category of some symmetric invariant bilinear forms over the t-nilpotent free Lie algebra with d generators. Taking into account this equivalence, t-nilpotent quadratic Lie algebras with d generators are classified (up to isometric isomorphisms, and over any field of characteristic zero), in the following cases: d = 2 and t ≤ 5, d = 3 and t ≤ 3.
Journal of Pure and Applied Algebra, 2008
In this paper some results on the Lie structure of prime superalgebras are discussed. We prove th... more In this paper some results on the Lie structure of prime superalgebras are discussed. We prove that, with the exception of some special cases, for a prime superalgebra, A, over a ring of scalars Φ with 1/2∈Φ, if L is a Lie ideal of A and W is a subalgebra of A such that [W, L]⊆ W, then either L⊆ Z or W⊆ Z. Likewise, if V is a submodule of A and [V, L]⊆ V, then either V⊆ Z or L⊆ Z or there exists an ideal of A, M, such that 0= [M,A]⊆ V. This work extends to prime superalgebras some results of I. N. Herstein, C. Lanski and S. Montgomery on prime algebras.
Proceedings of the American Mathematical Society, 2007
Proceedings of the American Mathematical Society, 2007
Communications in Algebra, Oct 8, 2009
J. M. Osborn described the simple algebras in which every nonzero symmetric element is invertible... more J. M. Osborn described the simple algebras in which every nonzero symmetric element is invertible, and semisimple algebras in which every symmetric element is either nilpotent or invertible. We give some analog theorems in superalgebras and results related with them.
A large number of algebraic structures, among which the associative and the Jordan algebras deser... more A large number of algebraic structures, among which the associative and the Jordan algebras deserve special mention, are closely related to the Lie algebras and to some interesting geometries. These relationships explain certain exceptional behaviors in Algebra and Geometry, which are nothing but manifestations of the same phenomena. In this note we analyze part of the research made during the last years by the research group of Algebra of the University of La Rioja. This research focuses on the study of non associative structures related to Lie algebras.