The Lie superalgebras in the extended Freudenthal Magic Square in characteristic 3 are shown to be related to some known simple Lie superalgebras, specific to this characteristic, constructed in… (More)

Some simple Lie superalgebras, specific of characteristic 3, defined by S. Bouarroudj and D. Leites [BL06], will be related to the simple alternative and commutative superalgebras discovered by I.P.… (More)

All gradings by abelian groups are classified on the following algebras over an algebraically closed field F: the simple Lie algebra of type G2 (charF = 2, 3), the exceptional simple Jordan algebra… (More)

Finite dimensional simple Jordan superalgebras over an algebraically closed field of characteristic zero were classified by V. Kac in 1977 [14], with one missing case that was later described by I.… (More)

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… (More)

Superinvolutions on graded associative algebras constitute a source of Lie and Jordan superalgebras. Graded versions of the classical Albert and Albert-Riehm Theorems on the existence of… (More)

The action of the symmetric group S4 on the Tetrahedron algebra, introduced by Hartwig and Terwilliger [HT05], is studied. This action gives a grading of the algebra which is related to its… (More)

Lie-Yamaguti algebras (or generalized Lie triple systems) are binary-ternary algebras intimately related to reductive homogeneous spaces. The Lie-Yamaguti algebras which are irreducible as modules… (More)

garcía de galdeano, seminario matemático, Alberto Elduque, TETRAHEDRON ALGEBRA

2006

The action of the symmetric group S4 on the Tetrahedron algebra, introduced by Hartwig and Terwilliger [HT05], is studied. This action gives a grading of the algebra which is related to its… (More)