Geometric Realizations of Lusztig’s Symmetries of Symmetrizable Quantum Groups

Hall Algebra Realizations of Quantum Groups

In particular, Q has finitely many indecomposables if and only if the underlying graph of Q is a disjoint union of copies of type ADE graphs. In this case, the above theorem is true for any field. Hence we can identify the isomorphism class of a representation over a Dynkin quiver with a function from the positive roots of ∆ to the nonnegative integers. The path algebra of Q is hereditary, so E...

Geometric Realizations of Substitutions

Nonlinear Realizations of Supersymmetry and Other Symmetries

Simultaneous nonlinear realizations of spontaneously broken supersym-metry in conjunction with other spontaneous and/or explicitly broken symmetries including R symmetry, global chiral symmetry, dilatations and the superconformal symmetries is reviewed. If supersymmetry (SUSY) is to be realized in nature, then it must be as a broken symmetry. Moreover, in order to be able to consistently gauge ...

Geometric Realizations of Polyhedral Complexes

We discuss two problems in combinatorial geometry. First, given a geometric polyhedral complex in R (a family of 3-polytopes attached face-to-face), can it always be realized over Q? We give a negative answer to this question, by presenting an irrational polyhedral complex with 1278 convex polyhedra. We then present a universality theorem on the space of realizations of such complexes. Second, ...

investigating the feasibility of a proposed model for geometric design of deployable arch structures

deployable scissor type structures are composed of the so-called scissor-like elements (sles), which are connected to each other at an intermediate point through a pivotal connection and allow them to be folded into a compact bundle for storage or transport. several sles are connected to each other in order to form units with regular polygonal plan views. the sides and radii of the polygons are...