TY - JOUR

T1 - Block-diagonalized rigidity matrices of symmetric frameworks and applications

AU - Schulze, Bernd

PY - 2010

Y1 - 2010

N2 - In this paper, we give a complete self-contained proof that the rigidity matrix of a symmetric bar and joint framework (as well as its transpose) can be transformed into a block-diagonalized form using techniques from group representation theory. This theorem is basic to a number of useful and interesting results concerning the rigidity and flexibility of symmetric frameworks. As an example, we use this theorem to prove a generalization of the symmetry-extended version of Maxwell's rule given in [FG] which can be applied to both injective and non-injective realizations in all dimensions.

AB - In this paper, we give a complete self-contained proof that the rigidity matrix of a symmetric bar and joint framework (as well as its transpose) can be transformed into a block-diagonalized form using techniques from group representation theory. This theorem is basic to a number of useful and interesting results concerning the rigidity and flexibility of symmetric frameworks. As an example, we use this theorem to prove a generalization of the symmetry-extended version of Maxwell's rule given in [FG] which can be applied to both injective and non-injective realizations in all dimensions.

M3 - Journal article

VL - 51

SP - 427

EP - 466

JO - Contributions to Algebra and Geometry

JF - Contributions to Algebra and Geometry

SN - 2191-0383

IS - 2

ER -