Triality and Bagger–Lambert theory

On the Triality Theory in Global Optimization

Triality theory is proved for a general unconstrained global optimization problem. The method adopted is simple but mathematically rigorous. Results show that if the primal problem and its canonical dual have the same dimension, the triality theory holds strongly in the tri-duality form as it was originally proposed. Otherwise, both the canonical min-max duality and the double-max duality still...

Pure Complementary Energy Principle and Triality Theory in Finite Elasticity

It is well-known that the complementary energy principle for large deformation elasticity was first proposed by Hellinger in 1914. Since Reissner clarified the boundary conditions in 1953, the complementary energy principles and methods in finite deformation mechanics have been studied extensively during the last forty years (cf. e.g. Koiter, 1976; Nemat-Nasser, 1977; Atluri, 1980; Lee & Shield...

Hopf Algebras with Triality

In this paper we revisit and extend the constructions of Glauberman and Doro on groups with triality and Moufang loops to Hopf algebras. We prove that the universal enveloping algebra of any Lie algebra with triality is a Hopf algebra with triality. This allows us to give a new construction of the universal enveloping algebras of Malcev algebras. Our work relies on the approach of Grishkov and ...

Finite deformation beam models and triality theory in dynamical post-buckling analysis1

Two new "nitely deformed dynamical beam models are established for serious study on non-linear vibrations of thick beams subjected to arbitrarily given external loads. The total potentials of these beam models are non-convex with double-well structures, which can be used in post-buckling analysis and frictional contact problems. Dual extremum principles in unstable dynamic systems are developed...

Lie Algebras with Triality