Search

Symmetry groups of Lie algebras and superalgebras constructed from (∈, δ)-Freudenthal-Kantor triple systems have been studied. In particular, for a special (ε, ε)-Freudenthal–Kantor triple, it is the SL(2) group. Also, the relationship between two constructions of Lie algebras from structurable algebras has been investigated. [ABSTRACT FROM PUBLISHER]

Left unital Kantor triple systems will be shown to coincide with the triple systems attached to structurable algebras endowed with an involutive automorphism, with triple product given by the formula. A related result is proved forFreudenthal-Kantor triple systems. Some consequences for the associated five-graded Lie algebras and superalgebras are deduced too. In particular, left unitalFreudenthal-Kantor triple systems are shown to be closely related to Lie superalgebras strictly graded over the root system of type. [ABSTRACT FROM PUBLISHER]

In this paper, we discuss a connection between (−1, −1)-Freudenthal–Kantor triple systems, anti-structurable algebras, quasi anti-flexible algebras and give examples of such structures. The paper provides the correspondence and characterization of a bilinear product corresponding a triple product. [ABSTRACT FROM AUTHOR]

In this paper we discuss the simplicity criteria of (-1, -1)-Freudenthal Kantor triple systems and give examples of such triple systems, from which we can construct some Lie superalgebras. We also show that we can associate a Jordan triple system to any (ϵ,δ)-Freudenthal Kantor triple system. Further, we introduce the notion of δ-structurable algebras and connect them to .(-1,δ)-Freudenthal Kantor triple systems and the corresponding Lie (super)algebra construction. [ABSTRACT FROM AUTHOR]

Abstract: 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 (respectively symmetric) group of degree 4. [Copyright &y& Elsevier]

It will be shown that general polynomials of the Kac–Moody field can generate either a new infinite-dimensional Lie algebra or W3 -type algebra, at least for the classical field case. For the case of the infinite dimensional Lie algebra, it leads to an infinite number of conserved classical quantities which generate hierarchy equations analogous to that of the KdV system. The chiral boson equation emerges as the lowest-order equation of the hierarchy. [ABSTRACT FROM AUTHOR]

Let L and L0 be a simple Lie algebra and its sub-Lie algebra, respectively. Then, a given irreducible representation ω of L decomposes into a direct sum of irreducible components of L0, which is called the branching rule. The general Dynkin indices introduced earlier satisfy many sum rules for the branching rule. These are found to be strong enough to uniquely determine the branching rule for many cases we have studied. The sum rules are especially useful for cases of exceptional Lie algebras. [ABSTRACT FROM AUTHOR]