Jordan property for non-linear algebraic groups and projective varieties

A century ago, Camille Jordan proved that the complex general linear group $GL_n(C)$ has the Jordan property: there is a Jordan constant $C_n$ such that every finite subgroup $H \le GL_n(C)$ has an abelian subgroup $H_1$ of index $[H : H_1] \le C_n$. We show that every connected algebraic group $G$ (which is not necessarily linear) has the Jordan property with the Jordan constant depending only on $\dim \, G$, and that the full automorphism group $Aut(X)$ of every projective variety $X$ has the Jordan propertyComment: American Journal of Mathematics (to appear); minor change

Generalized Conformal and Superconformal Group Actions and Jordan Algebras

We study the conformal groups of Jordan algebras along the lines suggested by Kantor. They provide a natural generalization of the concept of conformal transformations that leave 2-angles invariant to spaces where "p-angles" can be defined. We give an oscillator realization of the generalized conformal groups of Jordan algebras and Jordan triple systems(JTS). These results are extended to Jordan superalgebras and super JTS's. We give the conformal algebras of simple Jordan algebras, hermitian JTS's and the simple Jordan superalgebras as classified by Kac.Comment: 13 pp, IASSNS-HEP-92/8

Artinian algebras and Jordan type

The Jordan type of an element $\ell$ of the maximal ideal of an Artinian k-algebra A acting on an A-module M of k-dimension n, is the partition of n given by the Jordan block decomposition of the multiplication map $m_\ell$ on M. In general the Jordan type has more information than whether the pair $(\ell,M)$ is strong or weak Lefschetz. We develop basic properties of the Jordan type and their loci for modules over graded or local Artinian algebras. We as well study the relation of generic Jordan type of $A$ to the Hilbert function of $A$. We introduce and study a finer invariant, the Jordan degree type. In our last sections we give an overview of topics such as the Jordan types for Nagata idealizations, for modular tensor products, and for free extensions, including examples and some new results. We as well propose open problems.Comment: 53 pages. Added results, examples for Jordan degree type (Section 2.4) and Jordan type and initial ideal (Section 2.5

RDF, the semantic web, Jordan, Jordan and Jordan

This collection is addressed to archivists and library professionals, and so has a slight focus on implications implications for them. This chapter is nonetheless intended to be a more-or-less generic introduction to the Semantic Web and RDF, which isn't specific to that domain