Following recent advances in the local theory of current-algebraic orbifolds we present the basic dynamics including the twisted KZ equations of each twisted sector of all outer-automorphic WZW orbifolds on so(2n). Physics-friendly Cartesian bases are used throughout, and we are able in particular to assemble two Z3 triality orbifolds and three S3 triality orbifolds on so(8).

Abstract. The normal symmetric triality algebras (STA’s) and the normal Lie related triple algebras (LRTA’s) have been recently introduced by the second author, in connection with the principle of triality. It turns out that the unital normal LRTA’s are precisely the structurable algebras extensively studied by Allison. It will be shown that the normal STA’s (respectively LRTA’s) are the algebr...

We prove that in characteristic p > 0 a module with good filtration for a group of type E6 restricts to a module with good filtration for a group of type F4. Thus we confirm a conjecture of Brundan for one more case. Our method relies on the canonical Frobenius splittings of Mathieu. Next we settle the remaining cases, in characteristic not 2, with a computer-aided variation on the old method o...

Evans defined quasigroups equationally, and proved a Normal Form Theorem solving the word problem for free extensions of partial Latin squares. In this paper, quasigroups are redefined as algebras with six basic operations related by triality, manifested as coupled right and left regular actions of the symmetric group on three symbols. Triality leads to considerable simplifications in the proof...

Following an idea of Dadok, Harvey and Morgan, we apply the triality property of Spin(8) to calculate the comass of selfdual 4-forms on R. In particular, we prove that the Cayley form has comass 1 and that any self-dual 4-form realizing the maximal Wirtinger ratio (equation (1.5)) is SO(8)-conjugate to the Cayley form. We also use triality to prove that the stabilizer in SO(8) of the Cayley for...

Discrete symmetries in grand canonical ensembles and in ensembles canonical with respect to triality are investigated. We speculate about the general phase structure of finite temperature gauge theories with discrete Z(N) symmetry. Low and high temperature phases turn out to be different in both ensembles even for infinite systems. It is argued that gauge theories with matter fields in the fund...

We study affine Grassmannians for ramified triality groups. These groups are of type D43, so they forms the orthogonal or spin in 8 variables. They can be given as automorphisms certain twisted composition algebras obtained from octonion algebras. Using these algebras, we give descriptions functors classifying suitable lattices a fixed space.