Displaying similar documents to “Jordan- and Lie geometries”

Specializations of Jordan superalgebras.

Consuelo Martínez, Efim Zelmanov (2001)

RACSAM

Similarity:

We construct universal associative enveloping algebras for a large class of Jordan superalgebras.

Lie triple ideals and Lie triple epimorphisms on Jordan and Jordan-Banach algebras

M. Brešar, M. Cabrera, M. Fošner, A. R. Villena (2005)

Studia Mathematica

Similarity:

A linear subspace M of a Jordan algebra J is said to be a Lie triple ideal of J if [M,J,J] ⊆ M, where [·,·,·] denotes the associator. We show that every Lie triple ideal M of a nondegenerate Jordan algebra J is either contained in the center of J or contains the nonzero Lie triple ideal [U,J,J], where U is the ideal of J generated by [M,M,M]. Let H be a Jordan algebra, let J be a prime nondegenerate Jordan algebra with extended centroid C and unital central closure...

Distinguishing Jordan polynomials by means of a single Jordan-algebra norm

A. Moreno Galindo (1997)

Studia Mathematica

Similarity:

For = ℝ or ℂ we exhibit a Jordan-algebra norm ⎮·⎮ on the simple associative algebra M ∞ ( ) with the property that Jordan polynomials over are precisely those associative polynomials over which act ⎮·⎮-continuously on M ∞ ( ) . This analytic determination of Jordan polynomials improves the one recently obtained in [5].

Jordan superderivations and Jordan triple superderivations of superalgebras

He Yuan, Liangyun Chen (2016)

Colloquium Mathematicae

Similarity:

We study Jordan (θ,θ)-superderivations and Jordan triple (θ,θ)-superderivations of superalgebras, using the theory of functional identities in superalgebras. As a consequence, we prove that if A = A₀ ⊕ A₁ is a prime superalgebra with deg(A₁) ≥ 9, then Jordan superderivations and Jordan triple superderivations of A are superderivations of A, and generalized Jordan superderivations and generalized Jordan triple superderivations of A are generalized superderivations of A.

The Jordan structure of CSL algebras

Fangyan Lu (2009)

Studia Mathematica

Similarity:

We show that every Jordan isomorphism between CSL algebras is the sum of an isomorphism and an anti-isomorphism. Also we show that each Jordan derivation of a CSL algebra is a derivation.

A structure theory for Jordan H * -pairs

A. J. Calderón Martín, C. Martín González (2004)

Bollettino dell'Unione Matematica Italiana

Similarity:

Jordan H * -pairs appear, in a natural way, in the study of Lie H * -triple systems ([3]). Indeed, it is shown in [4, Th. 3.1] that the problem of the classification of Lie H * -triple systems is reduced to prove the existence of certain L * -algebra envelopes, and it is also shown in [3] that we can associate topologically simple nonquadratic Jordan H * -pairs to a wide class of Lie H * -triple systems and then the above envelopes can be obtained from a suitable classification, in terms of associative...