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Jesus Laliena

Publications and source records attributed to Jesus Laliena.

5 recordsLinked to original sources
arXiv2013

The derived superalgebra of skew elements of a semiprime superalgebra with superinvolution

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 \cap 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.

math.RA↗
arXiv2013

On the Lie structure of a prime associative superalgebra

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 $1/2\in Φ$, if $L$ is a Lie ideal of $A$ and $W$ is a subalgebra of $A$ such that $[W, L]\subseteq W$, then either $L\subseteq Z$ or $W\subseteq Z$. Likewise, if $V$ is a submodule of $A$ and $[V, L]\subseteq V$, then either $V\subseteq Z$ or $L\subseteq Z$ or there exists an ideal of $A$, $M$, such that $0\not= [M,A]\subseteq V$. This work extends to prime superalgebras some results of I. N. Herstein, C. Lanski and S. Montgomery on prime algebras.

math.RA↗
arXiv2007

Lie structure in semiprime superalgebrs with superinvolution

In this paper we investigate the Lie structure of the Lie superalgebra K of skew elements of a semiprime associative superalgebra A with superinvolution. We show that if U is a Lie ideal of K, then either there exists an ideal J of A such that a determined nonzero Lie ideal connected with J is 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.

math.RA↗
arXiv2006

Maximal subalgebras of Jordan superalgebras

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.

math.RA↗