On Jordan quadruple systems with quadripotents

The purpose of this article is to show the link between Jordan quadruple systems with quadripotents and Jordan algebras. We also extend the notions of the orthogonality, primitivity, and minimality of tripotents in a Jordan triple system to that of quadripotents in a Jordan quadruple system. We refine the Peirce decomposition of a Jordan quadruple system with respect to a quadripotent to be with respect to a system of orthogonal quadripotents and get the multiplication rules of the Peirce spaces. We show that the notions of primitive and minimal quadripotents coincide in a Jordan quadruple system.     

Bilipschitz homogeneous Jordan curves

We characterize bilipschitz homogeneous Jordan curves by utilizing quasihomogeneous parameterizations. We verify that rectifiable bilipschitz homogeneous Jordan curves satisfy a chordarc condition. We exhibit numerous examples including a bilipschitz homogeneous quasicircle which has lower Hausdorff density zero. We examine homeomorphisms between Jordan curves.

     

Jordan Algebras and Dual Affine Connections on Symmetric Cones

We study dually flat structures on symmetric cones associated with Jordan algebras. We give an interpretation of connections, a geometrical concept, in terms of Jordan algebras and show a relation between doubly autoparallel submanifolds and Jordan subalgebras.     

Jordan基的结构

用构造性方法证明了以同一个特征向量为终端向量的Jordan链从始端向量到终端向量可以有不同的最大长度,并给出了Jordan基中Jordan链的某些性质,进一步完善了Jordan标准形过渡矩阵求法的补充条件.     

Jordan基的结构

用构造性方法证明了以同一个特征向量为终端向量的Jordan链从始端向量到终端向量可以有不同的最大长度,并给出了Jordan基中Jordan链的某些性质,进一步完善了Jordan标准形过渡矩阵求法的补充条件.     

Homotope polynomial identities in prime Jordan systems

We prove an analogue of the Posner-Rowen theorem for strongly prime Jordan pairs and triple systems: the central closure of a strongly prime Jordan system satisfying a homotope polynomial identity is simple with finite capacity. We also prove that if a Jordan system satisfies a homotope polynomial identity it also satisfies a strict homotope polynomial identity.     

Compatibility criterion for quadripotents in Jordan quadruple systems

We extend the notion of compatibility of tripotents in a Jordan triple system to that of quadripotents in a Jordan quadruple system and get a criterion for compatibility of quadripotents in a Jordan quadruple system.     

Periodic jordan rings and order structure

The aim of this paper is to obtain information about a periodic Jordan ring by using only properties of its idempotent elements. Osborn proves that a power-associative periodic ring having only one nonzero idempotent element is a division ring. so associative. He also proves that a periodic Jordan ring is a subdirect product of simple periodic Jordan rings and that a simple periodic Jordan ring is either a periodic field or a Jordan ring of capacity 2. Using these results we obtain some necessary and suficient conditions for a periodic Jordan ring to be associative, and these conditions are only given in terms of the idempotent elements. We also characterize the periodic Jordan ring which are a direct product of periodic fields and simple periodic Jordan rings of capacity two.     

Reelle Jordanalgebren mit endlicher Spur

We study real Jordan algebras of arbitrary dimension which admit an associative, positive definite trace form and have suitable continuity properties. We construct certain completions until we arrive at a class of Jordan algebras corresponding to associative W^*-algebras of finite type. For these Jordan algebras we derive some basic properties concerning positive elements and idempotents. In contrast to other related investigations exceptional Jordan algebras are not excluded.     

Polynomial Identities and Nonidentities of Split Jordan Pairs

We show that split Jordan pairs over rings without 2-torsion can be distinguished by polynomial identities with integer coefficients. In particular, this holds for simple finite-dimensional Jordan pairs over algebraically closed fields of characteristic not 2. We also generalize results of Drensky and Racine and of Rached and Racine on polynomial identities of, respectively, Jordan algebras and Jordan triple systems.     

正压缩算子Jordan积的最大最小谱点

主要讨论了正压缩算子Jordan积的谱,刻画了正压缩算子Jordan积的最大最小谱点以及正交投影Jordan积的谱.     

Monodromy at Infinity and the Weights of Cohomology

We show that for a polynomial map, the size of the Jordan blocks for the eigenvalue 1 of the monodromy at infinity is bounded by the multiplicity of the reduced divisor at infinity of a good compactification of a general fiber. The existence of such Jordan blocks is related to global invariant cycles of the graded pieces of the weight filtration. These imply some applications to period integrals. We also show that such a Jordan block of size greater than 1 for the graded pieces of the weight filtration is the restriction of a strictly larger Jordan block for the total cohomology group. If there are no singularities at infinity, we have a more precise statement on the monodromy.     

On herstein's constructions relating jordan and associative superalgebras

We investigate the Jordan structure of a prime associative superalgebra and the Jordan structure of the symmetric elements of a *-prime associative superalgebra with superinvolution.     

Chain spaces over Jordan systems

Strong Jordan systems are certain subspaces of associative algebras closed under inversion and with many units. Every strong Jordan system gives rise to a chain space. We show that every homotopism of Jordan systems yields a morphism between the associated chain spaces and vice versa. By this, we obtain an isomorphy of categories.     

Special jordan pairs

There are some important Jordan pairs contained in the free associative pair, e.g. the free special Jordan pair and the Jordan pair of all symmetric elements under the reversal involution. We study the connection between these two Jordan pairs in the case when the ring of scalars contains ½.     

JORDAN–KRONECKER INVARIANTS OF FINITE-DIMENSIONAL LIE ALGEBRAS

For any finite-dimensional Lie algebra we introduce the notion of Jordan–Kronecker invariants, study their properties, and discuss examples. These invariants naturally appear in the framework of the bi-Hamiltonian approach to integrable systems on Lie algebras and are closely related to Mischenko–Fomenko’s argument shift method. We also state a generalised argument shift conjecture and prove it for many series of Lie algebras.     

Jordan operator algebras: basic theory

Jordan operator algebras are norm‐closed spaces of operators on a Hilbert space which are closed under the Jordan product. The discovery of the present paper is that there exists a huge and tractable theory of possibly nonselfadjoint Jordan operator algebras; they are far more similar to associative operator algebras than was suspected. We initiate the theory of such algebras.     

Jordan isomorphisms of triangular rings

We investigate Jordan isomorphisms of triangular rings and give a sufficient condition under which they are necessarily isomorphisms or anti-isomorphisms. As corollaries we obtain generalizations of two recent results: the one concerning Jordan isomorphisms of triangular matrix algebras by Beidar, Bresar and Chebotar, and the one concerning Jordan isomorphisms of nest algebras by Lu.