On the Specht property of varieties of commutative alternative algebras over a field of characteristic 3 and commutative Moufang loops.
On the structure of -algebras of type .
On the Structure of Reduced ...-Ternary Algebras of Degree > 2.
On unitary convex decompositions of vectors in a -algebra
By exploiting his recent results, the author further investigates the extent to which variation in the coefficients of a unitary convex decomposition of a vector in a unital -algebra permits the vector decomposable as convex combination of fewer unitaries; certain -algebra results due to M. Rørdam have been extended to the general setting of -algebras.
Operator-valued Bessel functions on Jordan algebras.
Peirce-Zerlegungen und Jordan-Strukturen zu homogenen Kegeln.
Poincaré duality for - Lie superalgebras
Positive projections and Jordan structure in operator algebras.
Prime nondegenerate Jordan algebras with nonzero socle and the symmetric Martindale algebra of quotients.
Projective homogeneous varieties birational to quadrics.
Propriétés analytiques du spèctre dans les algèbres de Jordan-Banach.
Pseudomonotonicity and related properties in Euclidean Jordan algebras.
Pure states on Jordan algebras
We prove that a pure state on a -algebras or a JB algebra is a unique extension of some pure state on a singly generated subalgebra if and only if its left kernel has a countable approximative unit. In particular, any pure state on a separable JB algebra is uniquely determined by some singly generated subalgebra. By contrast, only normal pure states on JBW algebras are determined by singly generated subalgebras, which provides a new characterization of normal pure states. As an application we contribute...
Quadro-quadric Cremona transformations in low dimensions via the -correspondence
It has been previously established that a Cremona transformation of bidegree (2,2) is linearly equivalent to the projectivization of the inverse map of a rank 3 Jordan algebra. We call this result the “-correspondence”. In this article, we apply it to the study of quadro-quadric Cremona transformations in low-dimensional projective spaces. In particular we describe new very simple families of such birational maps and obtain complete and explicit classifications in dimension 4 and 5.
Quelques applications géométriques des algèbres de Jordan
Quelques relations entre les algèbres de Jordan et les algèbres de Lie
Radikale von separablen Algebren über Ringen.
Range tripotents and order in JBW*-triples
In a JBW*-triple, i.e., a symmetric complex Banach space possessing a predual, the set of tripotents is naturally endowed with a partial order relation. This work is mainly concerned with this partial order relation when restricted to the subset 𝓡(A) of tripotents in a JBW*-triple B formed by the range tripotents of the elements of a JB*-subtriple A of B. The aim is to present recent developments obtained for the poset 𝓡(A) of the range tripotents relative to A, whilst also providing the necessary...
Real and Complex Noncommutative Jordan Banch Algebras.
Recent trends in the field of Jordan-Banach algebras