A Lie grading which is not a semigroup grading
This note is devoted to the construction of a graded Lie algebra, whose grading is not given by a semigroup.
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arXiv subjects
Alberto Elduque
Publications and source records attributed to Alberto Elduque.
The Kac Jordan superalgebra: automorphisms and maximal subalgebras
The group of automorphisms of the Kac Jordan superalgebra is described, and used to classify the maximal subalgebras.
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Lie algebras with S4-action and structurable algebras
The normal symmetric triality algebras (STA's) and the normal Lie related triple algebras (LRTA's) have been recently introduced by the second author, in connection with the principle of triality. It turns out that the unital normal LRTA's are precisely the structurable algebras extensively studied by Allison. It will be shown that the normal STA's (respectively LRTA's) are the algebras that coordinatize those Lie algebras whose automorphism group contains a copy of the alternating (resp. symmetric) group of degree 4.
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The Magic Square and Symmetric Compositions II
The construction of Freudenthal's Magic Square, which contains the exceptional simple Lie algebras, in terms of symmetric composition algebras is further developed here. The para-Hurwitz algebras, which form a subclass of the symmetric composition algebras, will be defined, in the split case, in terms of the natural two dimensional module for the simple Lie algebra sl(2). As a consequence, it will be shown how all the Lie algebras in Freudenthal's Magic Square can be constructed, in a unified way, using copies of sl(2) and of its natural module.
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New simple Lie superalgebras in characteristic 3
Symplectic (respectively orthogonal) triple systems provide constructions of Lie algebras (resp. superalgebras). However, in characteristic 3, it is shown that this role can be interchanged and that Lie superalgebras (resp. algebras) can be built out of symplectic triple systems (resp. orthogonal triple systems) with a different construction. As a consequence, new simple finite dimensional Lie superalgebras, as well as new models of some nonclassical simple Lie algebras, are obtained over fields of characteristic 3.
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(-1,-1)-Balanced Freudenthal Kantor triple systems and noncommutative Jordan algebras
A noncommutative Jordan algebra of a specific type is attached to any (-1,-1)-balanced Freudenthal Kantor triple system, in such a way that the triple product in this system is determined by the binary product in the algebra. Over fields of characteristic zero, the simple noncommutative Jordan algebras of this type are classified.
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A modified Brauer algebra as centralizer algebra of the unitary group
The centralizer algebra of the action of the unitary group on the real tensor powers of its natural module, is described by means of a modification in the multiplication of the signed Brauer algebras. The relationships of this algebra with the invariants for U(n), and with the decomposition of the above tensor powers into irreducible modules, is considered.
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Lie Superalgebras Graded by the Root System $A(m,n)$
We determine the Lie superalgebras that are graded by the root systems of the basic classical simple Lie superalgebras of type A$(m,n)$.
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