Triality principle for semisimilarities

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 ...

Lie Algebras with Triality

Degeneracy of Triality-symmetric Morphisms

We define a new symmetry for morphisms of vector bundles, called triality symmetry, and compute Chern class formulas for the degeneracy loci of such morphisms. In an appendix, we show how to canonically associate an octonion algebra bundle to any rank 2 vector bundle.

The Inclusion-Exclusion Principle for IF-States

Applying two definitions of the union of IF-events, P. Grzegorzewski gave two generalizations of the inclusion-exclusion principle for IF-events.In this paper we prove an inclusion-exclusion principle for IF-states based on a method which can also be used to prove Grzegorzewski's inclusion-exclusion principle for probabilities on IF-events.Finally, we give some applications of this principle by...